http://www.researchonline.mq.edu.au/vital/access/services/Feed ${session.getAttribute("locale")} 5 http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:17600 Historically, the subsistence based lifestyles of small scale economies (SSEs) have avoided pushing the stock of their natural resources beyond thresholds where their resilience could be lost. However, rising frequencies of natural disasters coupled with a growing outside influence from the developed economies are increasingly putting pressure on the economic and natural resources of these societies. This paper explores the nature and role of inter-linkages between ecological and economic resilience in SSEs towards maintaining long term sustainability in the face of these external influences. It is shown that initial conditions associated with the stock of natural and physical capital could be crucial factors in determining their successful transition towards higher economic growth without depleting their natural stock. When natural hazards pose risks of loss of natural capital, the rate of capital accumulation could increase or decrease depending upon the relation of such risks with natural and physical capital stocks. 2013-04-09T06:30:45.183Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:25052 To quantify the aggregrate losses from operational risk, we employ an actuarial risk model, ie, we consider compound Cox model of operational risk to deal with the stochastic nature of its frequency rate in real solutions. A shot noise process is used for this purpose. A compound Poisson model is also considered as its countrepart for the case where the operational loss frequency rate is deterministic. As the loss amounts arising due to mismanagement of operational risks are extremes in practice, we assume the loss sizes are log gamma, Frechet and truncated Gumbel. We also use an exponential distribution for the case of non-extreme losses. Employing a loss distribution approach, we derive the analytical/explicit forms of the Laplace transform of the distribution of aggregate operational losses. The value-at-risk and tail conditional expectation are used to evaluate the operational risk capital charge. Fast Fourier transform is used to approximate VaR and TCE numerically and the figures of the distributions of aggregate operational losses are provided. Numerical comparisons of VaR and TCE obtained using two compound processes are also made. 2013-04-02T23:21:50.198Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24774 For the additive risk model with time-varying covariates which are subject to measurement errors, we study the estimation of both regression parameters and cumulative baseline hazard function. We first develop a procedure to estimate the regression parameters by correcting the bias of the naive estimator, and provide the large-sample properties of the bias-adjusted estimators. The procedure can be repeated to further improve the accuracy of the estimator. We then construct a corresponding estimator for the cumulative baseline hazard function and derive its asymptotic properties. Based on these results, confidence bands are constructed for the cumulative hazard function as well as the survival function. Monte Carlo studies are conducted to evaluate the performance of these estimators. 2013-03-13T09:50:42.069Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24775 Applying the piecewise derteministic processes theory, the probability generating function of a Cox process, incorporating with shot noise process as the claim intensity, is obtained. We also derive the Laplace transform of the distribution of the shot noise process at claim jump times, using stationary assumption of the shot noise process at any times. Based on this Laplace transform and from the probability generating function of a Cox process with shot noise intensity, we obtain the distribution of the interval of a Cox process with shot noise intensity for insurance claims and its moments, that is, mean and variance. 2013-03-13T09:50:36.698Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24645 The Esscher transform is an important tool in actuarial science. Since the pioneering work of Gerber and Shiu (1994), the use of the Esscher transform for option valuation has also been investigated extensively. However, the relationships between the asset pricing model based on the Esscher transform and some fundamental equilibrium-based asset pricing models, such as consumption-based models, have so far not been well-explored. In this paper, we attempt to bridge the gap between consumption-based models and asset pricing models based on Esscher-type transformations in a discrete-time setting. Based on certain assumptions for the distributions of asset returns, changes in aggregate consumptions and returns on the market portfolio, we construct pricing measures that are consistent with those arising from Esscher-type transformations. Explicit relationships between the market price of risk, and the risk preference parameters are derived for some particular cases. 2013-03-11T21:11:22.288Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24668 In this paper we propose a semiparametric model to fit medical cost data with a proportion of zero cost values. In our model, the unknown cumulative cost is defined to be a function of the failure time to account for the correlation between the cost and the failure time. The nonparametric nature of the cost function allows full flexibility in matching the reality. Local likelihood estimation is proposed to estimate the unknown accumulative cost functions and the related parameters, and their asymptotic properties are investigated as well. Simulation studies are performed to illustrate our models and proposed methods. 2013-03-11T21:10:37.448Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24670 Motivated by a practical problem, [Z.W. Cai, P.A. Naik, C.L. Tsai, De-noised least squares estimators: An application to estimating advertising effectiveness, Statist. Sinica 10 (2000) 1231–1243] proposed a new regression model with noised variables due to measurement errors. In this model, the means of some covariates are nonparametric functions of an auxiliary variable. They also proposed a de-noised estimator for the parameters of interest, and showed that it is root-n consistent and asymptotically normal when undersmoothing is applied. The undersmoothing, however, causes difficulty in selecting the bandwidth. In this paper, we propose an alternative corrected de-noised estimator, which is asymptotically normal without the need for undersmoothing. The asymptotic normality holds over a fairly wide range of bandwidth. A consistent estimator of the asymptotic covariance matrix under a general stationary error process is also proposed. In addition, we discuss the fitting of the error structure, which is important for modeling diagnostics and statistical inference, and extend the existing error structure fitting method to this new regression model. A simulation study is made to evaluate the proposed estimators, and an application to a set of advertising data is also illustrated. 2013-03-11T21:10:33.098Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24672 In this paper, we study the estimation of the unbalanced panel data partially linear models with a one-way error components structure. A weighted semiparametric least squares estimator (WSLSE) is developed using polynomial spline approximation and least squares. We show that the WSLSE is asymptotically more efficient than the corresponding unweighted estimator for both parametric and nonparametric components of the model. This is a significant improvement over previous results in the literature which showed that the simply weighting technique can only improve the estimation of the parametric component. The asymptotic normalities of the proposed WSLSE are also established. Another focus of this paper is to provide a variable selection procedure to select significant covariates in the parametric part, based on a combination of the nonconcave penalization and the weighted semiparametric least squares. The proposed procedure simultaneously selects significant covariates and estimates unknown parameters. With a proper choice of regularization parameters and penalty function, the resulted estimator is shown to possess an oracle property. Simulation studies and an example of application on a set of hormone data are used to demonstrate this proposed procedure. 2013-03-11T21:10:28.338Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24673 Change-point hazard models have been extensively investigated by many authors, but the literature on change-point problems with survival data subject to censoring is rather small. In an earlier example provided by Matthews and Farewell (1982), a set of nonlymphoblastic leukemia data were fitted by using a change-point model. But for that data set, the Kaplan-Meier estimator of the distribution function levels off well below 1, which indicates the presence of "long-term survivors" in the data. In this paper, we propose a new change-point model for survival data that accounts for long-term survivors. Estimation methods for the proposed model are investigated, and large-sample properties of the estimators are established. A simulation study is carried out to evaluate the performance of the estimating methods. As an application, the nonlymphoblastic leukemia data are re-analyzed using the new model. 2013-03-11T21:10:26.004Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24571 We study option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of a stock depends on a finite state Markov chain. Using a minimal martingale measure we show that the risk minimizing option price satisfies a system of Black-Scholes partial differential equations with weak coupling. 2013-03-06T08:01:32.781Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7497 For insurance risks, jump processes such as homogeneous/non-homogeneous compound Poisson processes and compound Cox processes have been used to model aggregate losses. If we consider the economic assumption of a positive interest to aggregate losses, Lévy processes have proven to be useful. Also in financial modelling, it has been observed that diffusion models are not robust enough to capture the appearance of jumps in underlying asset prices and interest rates. As a result, jump diffusion processes, which are, simply speaking, combinations of compound Poisson processes with Brownian motion, have gained popularity for modelling in insurance and finance. In this paper, considering a jump diffusion process, we obtain the explicit expression of the joint Laplace transform of the distribution of a jump diffusion process and its integrated process, assuming that jump size follows the mixture of two exponential distributions, which is a special case of phase-type distributions. Based on this Laplace transform, we derive the moments of the aggregate accumulated claim amounts of insurance risk. For a financial application, we concern non-defaultable zero-coupon bond pricing. We also provide several numerical examples for the moments of aggregate accumulated claims and default-free zero-coupon bond prices. 2012-03-22T05:47:27.062Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16553 Building a science on the foundations of practitioners’ experimentation was one of Donald Schön’s abiding interests. This paper outlines a method of reflective practice research on which this kind of science can be built. Its basic elements are: (1) A focus on the “sense” practitioners make of their situations. This allows for a much richer explication of practitioners’ understanding. (2) Formally differentiating between kinds of reflective thinking to demonstrate rigorous reliance on our practice, as experienced, as we reflect. (3) Use of a non-standard logic and a distinctive grammar in describing the “sense” we make of our practice situations, as this enables a much more faithful rendering in models and theories of our sense of orientation. (4) A method of combining these in an experimental practice that enables models of practice traditions to evolve, taking in insights from innovative practice, and experiences from diverse cases. 2012-01-04T00:23:39.447Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16269 In this paper, we present a procedure for consistent estimation of the severity and frequency distributions based on incomplete insurance data and demonstrate that ignoring the thresholds leads to a serious underestimation of the ruin probabilities. The event frequency is modelled with a non- homogeneous Poisson process with a sinusoidal intensity rate function. The choice of an adequate loss distribution is conducted via the in-sample goodness-of-fit procedures and forecasting, using classical and robust methodologies. 2011-12-09T21:16:31.505Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16284 Using the large Hirulog and Early Reperfusion or Occlusion (HERO-2) trial a parsimonious multivariable model for 30-day mortality risk assessment in acute myocardial infarction (AMI) was developed. HERO-2 was an international randomized trial of two antithrombotic therapies–unfractionated heparin and bivalirudin–for the treatment of AMI. This trial recruited 17 073 patients from 46 countries from Europe, North and Latin America and Asia, including Australia, New Zealand and Russia. An important issue in applying findings from randomized clinical trials is the procedure to estimate risk among members of other patient populations. Methods for updating risk models for AMI are compared. Simple re-calibration (re-estimation of the intercept and slope of the linear predictor within regions) and model revision (re-estimation of all regression coefficients within regions) with and without shrinkage were compared to a global additive model with a built-in region effect. The relative performance of these methods in the different geographical regions, which vary in sample size, is of primary interest. Model revision only provided a slight improvement in predictive performance when applied with shrinkage in the smallest region Asia (N=756). In conclusion, a global model with regional re-calibration is adequate: region-specific coefficients did not provide worthwhile improvements in any region. 2011-12-09T21:15:54.960Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16383 We examine two bivariate skewdistributions, both of which generalize the bivariate symmetric distribution. The second, based on the bivariate skew normal distribution, always displays positive asymptotic lower taildependence. The difference is associated with the varying tail behavior of the marginals. 2011-12-09T21:10:41.376Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16127 Semi-Markov processes have gained popularity as multistate models of disease progression, but have rarely been used in randomised clinical trials (RCTs) when many endpoints are collected over time. Reasons for this include the additional complexity created by censoring, the complexity of the model usually characterised by transition intensities, and difficulties in estimating clinically relevant quantities. In this paper, we show that an indirect approach can address these issues, while accommodating censored data and permitting accurate estimation of survivor functions, hazard ratio and net reductions in risk. The technique combines saddlepoint approximation and likelihood theory to fit a semi-Markov model, specified in terms of its transition probabilities and moment-generating functions (MGFs). A key feature of this approach is that the proportional hazard (PH) assumption commonly assumed for all transition time distributions is no longer needed. Inference for clinically relevant quantities is obtained through bootstrapping or randomisation tests; a simple goodness of fit procedure exploiting the link with the cumulative incidence function for competing risks is also introduced. As illustration, an illness–death model (with transition times between randomisation, non-fatal stroke, and death) for a cardiovascular trial (LIPID) is provided. Evidence of a cumulative benefit of continued treatment, not identified by standard analysis methods in earlier published work, is presented. The technique is flexible enough to be applied extensively in clinical trials. 2011-11-28T10:00:33.151Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16128 For premium calculation principles or risk measures, all existing works only consider the additivity for a finite number of comonotonic risks. As we all know, a limiting status of finite additivity is the additivity for countable risks. In this paper we investigate the countable additivity and generate new and elegant characterizations for Choquet pricing and distortion premium principles. We also study the countable exchangeability, as an extension to additivity. It leads to generalized Choquet pricing and generalized distortion premium principles. 2011-11-28T10:00:30.968Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16131 In classical Bühlmann credibility models, claims are assumed to be independent between different risks. In many practical situations, however, this assumption may be violated because there are situations that could drive possible relationship among the insured individuals. This paper aims to extend the Bühlmann and Bühlmann–Straub credibility models to account for a special type of dependence between risks induced by common stochastic effects. By means of the projection method, the corresponding credibility premiums are obtained, which generalize some well known existing results in credibility theory. 2011-11-28T10:00:23.256Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16133 The estimation of loss reserves for incurred but not reported (IBNR) claims presents an important task for insurance companies to predict their liabilities. Conventional methods, such as ladder or separation methods based on aggregated or grouped claims of the so-called “run-off triangle”, have been illustrated to have some drawbacks. Recently, individual claim loss models have attracted a great deal of interest in actuarial literature, which can overcome the shortcomings of aggregated claim loss models. In this paper, we propose an alternative individual claim loss model, which has a semiparametric structure and can be used to fit flexibly the claim loss reserving. Local likelihood is employed to estimate the parametric and nonparametric components of the model, and their asymptotic properties are discussed. Then the prediction of the IBNR claim loss reserving is investigated. A simulation study is carried out to evaluate the performance of the proposed methods. 2011-11-28T10:00:21.641Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16135 This article discusses the determination of risk capital based on “aversion” functions. Aversion functions weigh different outcomes according to perceived severity. Many practical and popular risk measures are usefully viewed in terms of aversion functions including those arising from distortion operators and risk margin loadings. The approach of this paper builds on, unifies, and extends existing disparate approaches discussed in the literature. Analytical and computer generated illustrations are given as well as suggestions for the practical determination of aversion functions. 2011-11-28T10:00:17.966Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16119 Previously we used the geometry of n-dimensional space to derive the paired samples t-test and its p-value. In the present paper we describe the ‘ubiquitous’ application of these results to single degree of freedom linear model hypothesis tests. As examples, we derive the p- and t-values for the independent samples t-test, for testing a contrast in an analysis of variance and for testing the slope in a simple linear regression analysis. An angle θ in n-dimensional space is again pivotal in the development of the ideas. The relationships between p, t, θ, F and the correlation coefficient are also described by using a ‘statistical triangle’. 2011-11-28T03:40:33.799Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15673 We consider independent sampling from a two-component mixture distribution, where one component (called the parametric component) is from a known distributional family and the other component (called the non-parametric component) is unknown. This is a semi-parametric mixture distribution. We discretize the nonparametric component and estimate the parameters of this mixture model, namely the mixing proportion, the unknown parameters of the parametric component and the discretized non-parametric component. We define the maximum penalized likelihood (MPL) estimates of the mixture model parameters and then develop a generalized EM (GEM) iterative scheme to compute the MPL estimates. A simulation study and an example from biology are presented. 2011-10-25T05:53:30.050Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15364 A risk minimization problem is considered in a continuous-time Markovian regime-switching financial model modulated by a continuous-time, finite-state Markov chain. We interpret the states of the chain as different market regimes. A convex risk measure is used as a measure of risk and an optimal portfolio is determined by minimizing the convex risk measure of the terminal wealth. We explore the state of the art of the stochastic differential game to formulate the problem as a Markovian regime-switching version of a two-player, zero- sum stochastic differential game. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game is provided. 2011-10-11T17:50:15.119Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15223 We investigate an optimal portfolio selection problem in a continuous-time Markov-modulated financial market when an economic agent faces model uncertainty and seeks a robust optimal portfolio strategy. The key market parameters are assumed to be modulated by a continuous-time, finite-state Markov chain whose states are interpreted as different states of an economy. The goal of the agent is to maximize the minimal expected utility of terminal wealth over a family of probability measures in a finite time horizon. The problem is then formulated as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game between the agent and the market. We solve the problem by the Hamilton-Jacobi-Bellman approach. 2011-10-05T13:11:17.462Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15141 We introduce a novel approach to optimal investment–reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment–reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) solutions to the optimal investment–reinsurance problems and derive closed-form solutions to the problems. 2011-09-29T06:50:42.205Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15034 In this paper, we consider a game theoretic approach to option valuation under Markovian regime-switching models, namely, a Markovian regime-switching geometric Brownian motion (GBM) and a Markovian regime-switching jump-diffusion model. In particular, we consider a stochastic differential game with two players, namely, the representative agent and the market. The representative agent has a power utility function and the market is a “fictitious” player of the game. We also explore and strengthen the connection between an equivalent martingale measure for option valuation selected by an equilibrium state of the stochastic differential game and that arising from a regime switching version of the Esscher transform. When the stock price process is governed by a Markovian regime-switching GBM, the pricing measures chosen by the two approaches coincide. When the stock price process is governed by a Markovian regime-switching jump-diffusion model, we identify the condition under which the pricing measures selected by the two approaches are identical. 2011-09-23T14:20:41.746Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15036 In this paper, we develop an option valuation model when the price dynamics of the underlying risky asset is governed by the exponential of a pure jump process specified by a shifted kernel-biased completely random measure. The class of kernel-biased completely random measures is a rich class of jump-type processes introduced in [James, L.F., 2005. Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages. Ann. Statist. 33, 1771–1799; James, L.F., 2006. Poisson calculus for spatial neutral to the right processes. Ann. Statist. 34, 416–440] and it provides a great deal of flexibility to incorporate both finite and infinite jump activities. It includes a general class of processes, namely, the generalized Gamma process, which in its turn includes the stable process, the Gamma process and the inverse Gaussian process as particular cases. The kernel-biased representation is a nice representation form and can describe different types of finite and infinite jump activities by choosing different mixing kernel functions. We employ a dynamic version of the Esscher transform, which resembles an exponential change of measures or a disintegration formula based on the Laplace functional used by James, to determine an equivalent martingale measure in the incomplete market. Closed-form option pricing formulae are obtained in some parametric cases, which provide practitioners with a convenient way to evaluate option prices. 2011-09-23T14:20:38.180Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:14861 This article investigates the valuation of currency options when the dynamic of the spot Foreign Exchange (FX) rate is governed by a two-factor Markov-modulated stochastic volatility model, with the first stochastic volatility component driven by a lognormal diffusion process and the second independent stochastic volatility component driven by a continuous-time finite-state Markov chain model. The states of the Markov chain can be interpreted as the states of an economy. We employ the regime-switching Esscher transform to determine a martingale pricing measure for valuing currency options under the incomplete market setting. We consider the valuation of the European-style and American-style currency options. In the case of American options, we provide a decomposition result for the American option price into the sum of its European counterpart and the early exercise premium. Numerical results are included. 2011-09-08T20:20:34.276Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:14866 We consider the fair valuation of a participating life insurance policy with surrender options when the market values of the asset are modelled by Markov-modulated Geometric Brownian Motion (GBM). We reduce the dimension of the optimal stopping problem for the policy by changing probability measures. We also provide a decomposition result for the value of the policy. The Barone–Adesi–Whaley approximation has been employed to approximate the solution of the free boundary problem for the policy by second-order piecewise linear ordinary differential equations (ODEs). The fair valuation of participating perpetual American contracts are also considered. 2011-09-08T20:20:22.216Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:14869 We consider the pricing of options when the dynamics of the risky underlying asset are driven by a Markov-modulated jump-diffusion model. We suppose that the market interest rate, the drift and the volatility of the underlying risky asset switch over time according to the state of an economy, which is modelled by a continuous-time Markov chain. The measure process is defined to be a generalized mixture of Poisson random measure and encompasses a general class of processes, for example, a generalized gamma process, which includes the weighted gamma process and the inverse Gaussian process. Another interesting feature of the measure process is that jump times and jump sizes can be correlated in general. The model considered here can provide market practitioners with flexibility in modelling the dynamics of the underlying risky asset. We employ the generalized regime-switching Esscher transform to determine an equivalent martingale measure in the incomplete market setting. A system of coupled partial-differential-integral equations satisfied by the European option prices is derived. We also derive a decomposition result for an American put option into its European counterpart and early exercise premium. Simulation results of the model have been presented and discussed. 2011-09-08T20:20:20.722Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:14483 7 page(s) 2011-08-13T04:41:24.452Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:14395 In this paper, we highlight some qualitative facets of the discipline of statistics and argue that a qualitative approach, in particular a qualitative methodology known as phenomenography, allows us to research important aspects of statistics pedagogy. We summarize several components of our recent research into students' conceptions of statistics, their learning of statistics, our teaching of statistics, and their perceptions of their future professional work. We have obtained this information on the basis of analyses of several series of interviews with students studying statistics, both as statistics majors and as service students. In each of these cases, the broadest views relate in some way to personal connection, growth, and change. In other words, they contain a strong ontological component—focusing on being or becoming a statistician—above and beyond the standard epistemological component—focusing on the knowledge required to do statistics. We discuss the importance of personal change in becoming a statistician, or an informed professional user of statistics, and investigate the pedagogical conditions under which such change is likely to occur. 2011-08-09T12:03:25.689Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:13783 In this article, we propose a class of Box-Cox transformation models for recurrent event data, which includes the proportional means models as special cases. The new model offers great flexibility in formulating the effects of covariates on the mean functions of counting processes while leaving the stochastic structure completely unspecified. For the inference on the proposed models, we apply a profile pseudo-partial likelihood method to estimate the model parameters via estimating equation approaches and establish large sample properties of the estimators and examine its performance in moderate-sized samples through simulation studies. In addition, some graphical and numerical procedures are presented for model checking. An example of application on a set of multiple-infection data taken from a clinic study on chronic granulomatous disease (CGD) is also illustrated. 2011-06-24T23:30:40.969Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:13326 The lattice A*n is an important lattice because of its covering properties in low dimensions. Two algorithms exist in the literature that compute the nearest point in the lattice A*n in O(n log n) arithmetic operations. In this paper we describe a new algorithm that requires only O(n) operations. The new algorithm makes use of an approximate sorting procedure called a bucket sort. This is the fastest known nearest point algorithm for this lattice. 2011-05-25T21:38:33.611Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12219 We investigate two approaches, namely, the Esscher transform and the extended Girsanov’s principle, for option valuation in a discrete-time hidden Markov regime-switching Gaussian model. The model’s parameters including the interest rate, the appreciation rate and the volatility of a risky asset are governed by a discrete-time, finite-state, hidden Markov chain whose states represent the hidden states of an economy. We give a recursive filter for the hidden Markov chain and estimates of model parameters using a filter-based EM algorithm. We also derive predictors for the hidden Markov chain and some related quantities. These quantities are used to estimate the price of a standard European call option. Numerical examples based on real financial data are provided to illustrate the implementation of the proposed method. 2011-03-21T05:02:11.865Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12216 This paper is concerned with the statistical inference on seemingly unrelated varying coefficient partially linear models. By combining the local polynomial and profile least squares techniques, and estimating the contemporaneous correlation, we propose a class of weighted profile least squares estimators (WPLSEs) for the parametric components. It is shown that the WPLSEs achieve the semiparametric efficiency bound and are asymptotically normal. For the non-parametric components, by applying the undersmoothing technique, and taking the contemporaneous correlation into account, we propose an efficient local polynomial estimation. The resulting estimators are shown to have mean-squared errors smaller than those estimators that neglect the contemporaneous correlation. In addition, a class of variable selection procedures is developed for simultaneously selecting significant variables and estimating unknown parameters, based on the non-concave penalized and weighted profile least squares techniques. With a proper choice of regularization parameters and penalty functions, the proposed variable selection procedures perform as efficiently as if one knew the true submodels. The proposed methods are evaluated using wide simulation studies and applied to a set of real data. 2011-03-21T05:02:11.603Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12217 Two-sample comparison of survival times with “cured patients” is of major interest and a challenging issue in many areas, particularly in cancer clinical research. Recently, several authors have proposed various procedures of comparison, including tests of no overall, no short-term and no long-term differences between two samples. In clinical practice, it is often of interest to detect the difference in treatment effects among noncured patients regardless of the difference between cure fractions. In this paper, we propose a statistical test to compare two samples with cured patients and possibly heterogeneous treatment effects based on a class of semi-parametric transformation models, and our main focus is on the survival times of noncured patients. The empirical and quantile processes are used to construct strong approximations for the empirical curves. The two-sample test is then constructed from general least squares estimators derived from these processes. Simulation results show that the proposed test perform well. As an example of application, a set of bladder cancer data is analyzed to illustrate the proposed methods. 2011-03-21T05:02:07.839Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12218 Semiparametric transformation model has been extensively investigated in the literature. The model, however, has little dealt with survival data with cure fraction. In this article, we consider a class of semi-parametric transformation models, where an unknown transformation of the survival times with cure fraction is assumed to be linearly related to the covariates and the error distributions are parametrically specified by an extreme value distribution with unknown parameters. Estimators for the coefficients of covariates are obtained from pseudo Z-estimator procedures allowing censored observations. We show that the estimators are consistent and asymptotically normal. The bootstrap estimation of the variances of the estimators is also investigated. 2011-03-21T05:02:07.823Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12220 We consider a panel data semiparametric partially linear regression model with an unknown parameter vector for the linear parametric component, an unknown nonparametric function for the nonlinear component, and a one-way error component structure which allows unequal error variances (referred to as heteroscedasticity). We develop procedures to detect heteroscedasticity and one-way error component structure, and propose a weighted semiparametric least squares estimator (WSLSE) of the parametric component in the presence of heteroscedasticity and/or one-way error component structure. This WSLSE is asymptotically more efficient than the usual semiparametric least squares estimator considered in the literature. The asymptotic properties of the WSLSE are derived. The nonparametric component of the model is estimated by the local polynomial method. Some simulations are conducted to demonstrate the finite sample performances of the proposed testing and estimation procedures. An example of application on a set of panel data of medical expenditures in Australia is also illustrated. 2011-03-21T05:02:03.419Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12237 11 page(s) 2011-03-21T05:01:21.767Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12254 Identity link Poisson regression is useful when the mean of a count variable depends additively on a collection of predictor variables. It is particularly important in epidemiology, for modeling absolute differences in disease incidence rates as a function of covariates. A complication of such models is that standard computational methods for maximum likelihood estimation can be numerically unstable due to the nonnegativity constraints on the Poisson means. Here we present a straightforward and flexible method that provides stable maximization of the likelihood function over the constrained parameter space. This is achieved by conducting a sequence of maximizations within subsets of the parameter space, after which the global maximum is identified from among the subset maxima. The method adapts and extends EM algorithms that are useful in specialized applications involving Poisson deconvolution, but which do not apply in more general regression contexts. As well as allowing categorical and continuous covariates, the method has the flexibility to accommodate covariates with an unspecified isotonic form. Its computational reliability makes it particularly useful in bootstrap analyses, which may require stable convergence for thousands of implementations. Computations are illustrated using epidemiological data on occupational mortality, and biological data on crab population counts. This article has supplementary material online. 2011-03-21T05:00:32.679Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:11913 Courses taught in Applied Statistics, such as regression or multivariate analysis, tend to have the examination component based on a final written paper, either with computer output attached for interpretation or with summary statistics given so the calculator can be used to evaluate test statistics and hence make inference, or a mixture of both. Assignments may be based on students using a statistical package to do the analysis. The authors found this approach unsatisfactory. The first author trialled at the University of Canberra in 2001 both a mid semester computer based examination and final computer based examination with the students being allowed to use a variety of statistical packages. Student feedback was so favourable that she taught the course the following year in the same manner as well as a regression course. When she moved to Macquarie University she split the final examination for the third year regression course she was in charge of in 2004, 2005 and 2006 into a computer laboratory examination and a separate written paper. We have been unable to find more than a small number of other examples of this approach, which seems to have considerable promise as a way of implementing authentic assessment in applied courses. As well as case studies, issues associated with setting, running and marking such examinations are discussed. 2011-02-22T23:10:09.377Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9656 Cartoons by Roger Harvey. 2010-10-08T05:01:15.840Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9257 Occurrences of cyanobacterial abundance and their consequence in toxin produced by the bloom-forming cyanobacterium Microcystis aeruginosa were studied based on the data collected from 2003 to 2005 in the Wingecarribee reservoir, New South Wales, Australia. Environmental conditions associated with cyanobacterial abundance were high pH, low dissolved oxygen, low light penetration, high total nitrogen, and low nitrate/nitrite-nitrogen and ammonium-nitrogen (p-values < 0.05, r² = 0.80). Total nitrogen was found to be a nutrient limiting for cyanobacterial abundance in this reservoir rather than total phosphorous. The toxic bloom-forming cyanobacterium M. aeruginosa was most dominant in summer 2004 and autumn 2005 when a ratio of total nitrogen to total phosphorous was high (95%CI: 19.81--23.96) due to low total phosphorous concentration (95%CI: 18--24 μg per litre). However, microcystin concentration was detected only in summer 2004 despite high toxic bloom-forming cyanobacterium M. aeruginosa at the time. Our study suggested that the formation of toxic or non-toxic cyanobacterial blooms in the reservoir was associated more with nitrogen than with phosphorous and toxic cyanobacterial bloom was influenced by high ratio of total nitrogen to total phosphorous and ammonium-nitrogen. Microcystin concentration may not be a good indicator for M. aeruginosa dominance. 2010-08-23T12:50:39.400Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9259 Our recent research investigated the experiences of educators teaching statistics as service courses at universities. We conducted interviews by email with participants from many countries and whose teaching reflects diverse settings, student groups and disciplines-a microcosm of higher education today. We now focus on the tools, artefacts and resources respondents identified as critical to developing their teaching. These include computer and internet technology; data sets, texts and research and human resources, such as master teachers or teaching pools. Teacher development can be characterised as "the enhancement of the knowledge and capabilities to function as a teacher" (Gordon & Fittler, 2004) and is bound up with student learning. Hence tools and artefacts harnessed by educators to develop their teaching are resources for enhancing student learning. Our approach draws on activity theory, based on the work of Vygotsky, Leont'ev and colleagues, and emphasising mastering tools in collective and individual development. Vygotsky extended the idea of physical tools as mediators of change to psychological tools or mental tools. Case studies from our investigation are used to explore how the educators constitute their teaching identities in relation to cultural tools. 2010-08-23T12:50:39.262Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9252 A need was identified for a statistical learning system that combines a statistical package offering all standard statistical procedures together with a system that helps students to learn the rudiments of statistics through experiential learning. The WebStat Data Analysis and Learning System, a web-based student learning system, is designed to fulfill this need. Currently, the system can handle large data sets from a range of sources and perform all standard and commonly used statistical procedures such as descriptive statistics, regression analyses, and more sophisticated statistical modelling such as Generalised Linear Models (GLM). WebStat utilises the program R, one of the most sophisticated and extensive statistical programs available. It can be used by many students, particularly non-statistics research students. WebStat can be further developed to suit a wide range of users. In this paper, we describe and discuss the advantages of using WebStat as a learning tool, along with identifying the main features of and possible improvements to the current design. 2010-08-20T22:20:20.124Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9253 We introduce a method for modelling a continuous response which is the sum of a random number of terms. Examples are total insurance claim sizes (the total of all claims on a policy in a year), or total amount spent by credit card holders in a sector in a month, where there may be multiple spending episodes. The distribution of the number of terms may be, in principle, any discrete distribution defined on the non-negative integers; and each term has a continuous, right-skewed distribution. The resulting marginal distribution of the total amount is a mixed discrete-continuous model, with a probability mass at zero and a continuous component. The model explicitly specifies log-linear models for the four parameters in the total amount distribution. It may be fitted to data using a package written in R. The method is illustrated on an Australian motor vehicle insurance data set. 2010-08-20T22:20:10.599Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9254 In Vitro Fertilization (IVF) offers infertile couples the opportunity to have a baby. Many of these couples have multiple attempts to try to achieve this goal. To model the risk factors that affect the process at any of its stages, across the multiple attempts, an ordinal response and an extended continuation ratio random effects model have been used. This enabled the modelling of differential effects of covariates on different stages of the process. A significant random effect suggests that there is a couple specific effect, which may be interpreted as a fertility index. 2010-08-20T22:20:08.664Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9141 We Propose a Model for Valuing Participating Life Insurance Products under a Generalized jump-diffusion Model with a Markov-switching Compensator. It also Nests a Number of Important and Popular Models in Finance, Including the Classes of jump-diffusion Models and Markovian regime-switching Models. The Esscher Transform is Employed to Determine an Equivalent Martingale Measure. Simulation Experiments are Conducted to Illustrate the Practical Implementation of the Model and to Highlight some Features that can be Obtained from our Model. 2010-08-09T09:00:21.998Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9078 This paper refers to a graph called grapharti which I have developed. Grapharti is designed to organise and display large amounts of data obtained from surveys, opinion polls, course/teacher evaluations, sports and the stock market. The data are retrieved from a database and displayed on a web page. The purpose of this paper is to show that grapharti can encourage exploration of and facilitate insight into large amounts of data, and thus be used as a tool in statistical education. Users of grapharti are enticed to explore the data and this in turn results in reflection on the data. With the focus on the graph and the data, the user can visualise some statistical concepts in a new manner. 2010-08-03T21:10:40.304Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7681 This article explores alternative state space representations for ARMA models. We advocate representations that have minimal state order and appealing Kalman filter steady state properties. We derive expressions for smoother output and describe concrete connections to classical infinite sample representations. 2010-04-08T03:50:05.492Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7657 Generalised linear models have proved increasingly useful in traffic accident modelling since their first appearance in this context in the 1980s. Such models are used, for example, in the development of standards and in the isolation of locations where improvements should be made. The aim of this paper to describe traffic accident modelling in tandem with scientific method and thus to set it in its natural context. Four steps in one cycle of the modelling process can be identified: variable selection and measurement, model fitting, goodness of fit testing and finally, development of confidence intervals and prediction intervals. Appropriate tools for the latter two steps have been developed recently and are described. The paper illustrates the cycle with a real example. 2010-04-01T14:01:15.585Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7520 This paper deals with the problem of interval estimation of the scale parameter in the two-parameter exponential distribution subject to Type II double censoring. Base on a Type II doubly censored sample, we construct a class of interval estimators of the scale parameter which are better than the shortest length affine equivariant interval both in coverage probability and in length. The procedure can be repeated to make further improvement. The extension of the method leads to a smoothly improved confidence interval which improves the interval length with probability one. All improved intervals belong to the class of scale equivariant intervals. 2010-03-23T13:41:48.729Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7504 We consider a panel data semiparametric partially linear regression model with an unknown vector β of regression coefficients, an unknown nonparametric function g(·) for nonlinear component, and unobservable serially correlated errors. The correlated errors are modeled by a vector autoregressive process which involves a constant intraclass correlation. Applying the pilot estimators of β and g(·), we construct estimators of the autoregressive coefficients, the intraclass correlation and the error variance, and investigate their asymptotic properties. Fitting the error structure results in a new semiparametric two-step estimator of β, which is shown to be asymptotically more efficient than the usual semiparametric least squares estimator in terms of asymptotic covariance matrix. Asymptotic normality of this new estimator is established, and a consistent estimator of its asymptotic covariance matrix is presented. Furthermore, a corresponding estimator of g(·) is also provided. These results can be used to make asymptotically efficient statistical inference. Some simulation studies are conducted to illustrate the finite sample performances of these proposed estimators. 2010-03-22T08:10:25.449Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7512 For premium calculation principles or risk measures, all existing works only consider the additivity for a finite number of comonotonic risks. As we all know, a limiting status of finite additivity is the additivity for countable risks. In this paper we investigate the countable additivity and generate new and elegant characterizations for Choquet pricing and distortion premium principles. We also study the countable exchangeability, as an extension to additivity. It leads to generalized Choquet pricing and generalized distortion premium principles. 2010-03-22T08:10:11.133Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7440 Students in the same statistics course learn different things, and view the role of the lecturer in different ways. We report on empirical research on students’ conceptions of learning statistics, their expectations of teaching, and the relationship between them. The research is based on interviews, analysed using a qualitative methodology, with statistics students studying for a mathematics degree. Students expressed a range of conceptions of learning in statistics and a range of conceptions of their lecturers’ teaching. These conceptions of learning and teaching were related, but not as closely or as exclusively as previous researchers have indicated. Looking at what students expect of teachers and their views of their own learning provides an opportunity for teachers to develop teaching practices that challenge students to move towards more integrated conceptions of statistics learning. 2010-03-19T02:31:04.554Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7400 Discrete-time survival data typically possess three features: discreteness, ties, and concomitant information, which require appropriate discrete-time models to analyze. In this paper, we first review some existing discrete-time survival models and then extend them to discrete-time cure survival models, which account for the presence of long-term survivors (cured individuals). The maximum likelihood estimation as well as approximate partial likelihood approaches are used to estimate the model parameters. Simulation results are shown to support the suitability of such models for discrete-time survival data with long-term survivors. An example of applications on a set of bladder tumor recurrence data is also presented. 2010-03-16T07:20:36.580Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7411 The smoothing filter is appropriately modified for state space models with an unknown initial condition. Modifications are confined to an initial stretch of the data. An application illustrates procedures. 2010-03-16T07:20:09.762Z ]]>