THE EPIDEMIOLOGY OF A DISEASE USING HAZARD FUNCTIONS1

A prime objective of this paper is to mathematically quantify certain epidemiological concepts and show how some of these can be applied to certain registry type data. Usually epidemiological quantities are expressed in terms of density functions. However it is often more natural to estimate hazard functions in practical situations. Hence the emphasis will be on expressing various measures in terms of hazard functions. This contrasts with the useful paper of Albert, Gertman & Louis (1978) where density functions are used throughout. The definitions of some key concepts such as cohort effect are also different which gives rise to an alternative analysis and some new results. Initially, incidence, mortality and prevalence are discussed and this is followed by a treatment of initiation which is a less commonly used measure. The results are applied to the lung cancer data in the South Australian Central Cancer Registry.     

Nonstationary panel data analysis: an overview of some recent developments

This paper overviews some recent developments in panel data asymptotics, concentrating on the nonstationary panel case and gives a new result for models with individual effects. Underlying recent theory are asymptotics for multi-indexed processes in which both indexes may pass to infinity. We review some of the new limit theory that has been developed, show how it can be applied and give a new interpretation of individual effects in nonstationary panel data. Fundamental to the interpretation of much of the asymptotics is the concept of a panel regression coefficient which measures the long run average relation across a section of the panel. This concept is analogous to the statistical interpretation of the coefficient in a classical regression relation. A variety of nonstationary panel data models are discussed and the paper reviews the asymptotic properties of estimators in these various models. Some recent developments in panel unit root tests and stationary dynamic panel regression models are also reviewed.     

Nonstationary panel data analysis: an overview of some recent developments

This paper overviews some recent developments in panel data asymptotics, concentrating on the nonstationary panel case and gives a new result for models with individual effects. Underlying recent theory are asymptotics for multi-indexed processes in which both indexes may pass to infinity. We review some of the new limit theory that has been developed, show how it can be applied and give a new interpretation of individual effects in nonstationary panel data. Fundamental to the interpretation of much of the asymptotics is the concept of a panel regression coefficient which measures the long run average relation across a section of the panel. This concept is analogous to the statistical interpretation of the coefficient in a classical regression relation. A variety of nonstationary panel data models are discussed and the paper reviews the asymptotic properties of estimators in these various models. Some recent developments in panel unit root tests and stationary dynamic panel regression models are also reviewed.     

“长三角”制造业经济拉动力分析

制造业是拉动长江三角洲经济发展的主要源动力.为了更加准确的界定制造业在长江三角洲产业发展中的拉动作用,论文深入分析了长江三角洲16个城市的制造业和经济发展水平之间的关系,揭示了长三角地区制造业经济拉动力的变化及其影响因素,指出:虽然长三角制造业从总体上具有较强大的经济拉动力,但其内部各行业之间仍然具有明显的差异,并由此表现出制造业经济拉动力的某螳具体特征.文章最后从长江三角洲制造业引申开来,阐述了促进我国制造业发展、进一步强化制造业经济拉动作用的新思路.     

Effect of correlation on the estimation of a mean in the presence of spurious observations

This paper examines the effect of correlation of observations on estimators of a mean which are designed to guard against the possibility of spurious observations (that is, observations generated in a manner not intended). The mean squared error, premium and protection of these estimators are evaluated and discussed for some specific correlation structures.     

Selected Ranked Set Sampling

This paper proposes a sampling procedure called selected ranked set sampling (SRSS), in which only selected observations from a ranked set sample (RSS) are measured. This paper describes the optimal linear estimation of location and scale parameters based on SRSS, and for some distributions it presents the required tables for optimal selections. For these distributions, the optimal SRSS estimators are compared with the other popular simple random sample (SRS) and RSS estimators. In every situation the estimators based on SRSS are found advantageous at least in some respect, compared to those obtained from SRS or RSS. The SRSS method with errors in ranking is also described. The relative precision of the estimator of the population mean is investigated for different degrees of correlations between the actual and erroneous ranking. The paper reports the minimum value of the correlation coefficient between the actual and the erroneous ranking required for achieving better precision with respect to the usual SRS estimator and with respect to the RSS estimator.     

Questions & Answers

Several methods are available for finding minimum variance unbiased estimators for functions of distribution parameters. This paper concentrates on two which are rarely used but simple when applicable. The first, previously discussed by Davis (1951) and Tate (1959), yields estimators by differentiation when the range of nonzero probability for a continuous random variable depends on an unknown parameter. The second, which has wider applicability, permits estimators for some rather complicated functions to be found by using some well-known results from distribution theory. A number of examples are presented, many of which are suitable for classroom exercises.     

A Versatile Birth—Death Model Applicable to Four Distinct Problems

This paper revisits a simple birth–death model which arises in slightly different forms in four distinct stochastic problems. These are the barbershop queue, coupon collecting, vocabulary usage and geological dating. Discrete and continuous time Markov chains are used to characterize these problems. Somewhat different questions are posed for each particular case, and practical results are derived for each process. The paper concludes with some comments on the versatility of this applied probability model.     

On the importance of being smooth

This paper makes the proposition that the only statistical analyses to achieve widespread popular use in statistical practice are those whose formulations are based on very smooth mathematical functions. The argument is made on an empirical basis, through examples. Given the truth of the proposition, the question ‘why should it be so?’ is intriguing, and any discussion has to be speculative. To aid that discussion, the paper starts with a list of statistical desiderata, with the view of seeing what properties are provided by underlying smoothness. This provides some rationale for the proposition. After that, the examples are considered. Methods that are widely used are listed, along with other methods which, despite impressive properties and possible early promise, have languished in the arena of practical application. Whatever the underlying causes may be, the proposition carries a worthwhile message for the formulation of new statistical methods, and for the adaptation of some of the old ones.     

The efficacy of the correlation dimension technique in detecting determinism in small samples

This paper presents the results of a simulation study investigating the efficacy of the correlation dimension technique in detecting the presence of deterministic structure in small data sets. The results show that for some very simple structures a mere 100 data points suffice; but for some slightly more complicated structures, which arguably are still simple relative to real-world structures, even 2500 data points are inadequate. These results suggest that substantial caution be used in interpreting negative results on empirical data.     

Theory & Methods: Incomplete detection in enumeration surveys: Whither distance sampling?

This paper considers the problem of undercount or incomplete detection in enumeration surveys that are intended to estimate population counts or population abundance. The problem is widespread in ecology but also occurs in other surveys: the census undercount is a well-known example of the problem. After framing the problem in a general context, the paper focuses on line transect sampling and the distance sampling method which has been widely applied in surveys of ecological populations. It describes distance sampling data and presents a graphical derivation of the distance sampling estimator. The graphical analysis leads to a new expression for the distance sampling estimator which gives useful insights into the nature of the estimator. The paper discusses the uniformity assumption on which distance sampling depends and describes the properties of the distance sampling estimator when uniformity does not hold. It then explores the relationship between this and other evaluations of distance sampling and mentions briefly some statistical ideas for treating the general incomplete detection problem. The paper concludes with some reflections on general insights arising from the research.     

Bayesian forecasting for AR(1) models with normal coefficients

This paper presents a Bayesian solution to the problem of time series forecasting, for the case in which the generating process is an autoregressive of order one, with a normal random coefficient. The proposed procedure is based on the predictive density of the future observation. Conjugate priors are used for some parameters, while improper vague priors are used for others.     

Representations of the covariance matrix for robustness in the gauss-markov model

This paper considers some extensions of the results of Rao and Rao and Mitra. They gave a table of general representations of the covariance matrix in terms of the given design matrix, under which various statistical procedures in the least squares theory based on the simple Gauss-Markov model with the spherical covariance matrix are also valid under the general Gauss-Markov model. We shall give extended tables adding some more results relating to robustness, especially in connection with the estimation and testing of hypotheses on linear parametric functions     

A study on the use of belief functions for medical expert systems

This paper describes methods for extracting belief functions from data and incorporating expert opinions. The techniques are applied to a medical domain involving the diagnosis of diferent types of liver diseases. This is a domain in which experts are poor at predicting precise (singleton) outcomes. The methodology developed is shown to perform considerably better than the experts alone. Several methods by which to find belief functions from data are compared, and some methods proposed here are shown to outperform a suggestion by Shafer. The system has been fully implemented on a SEQUENT parallel machine and has a user interface which is simple to use and allows for changes and questions.     

Chaos: But Not in Both Directions!

This paper will informally explore the reversal of some stochastic autoregressive processes, which lead to deterministically chaotic processes. Correspondingly, the stochastic reversal of map models is shown to lead to a new class of invariant distribution. Finally, some connections between congruential recursions and independence in discretized chaotic processes are illustrated.     

Point-symmetry models and decomposition for collapsed square contingency tables

For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed tables with some adjacent categories combined in the original table. This paper proposes three kinds of new models which have the structure of point-symmetry (PS), quasi point-symmetry and marginal point-symmetry for collapsed square tables. This paper also gives a decomposition of the PS model for collapsed square tables. The father's and his daughter's occupational mobility data are analyzed using new models.     

Local Whittle likelihood approach for generalized divergence

There are many approaches in the estimation of spectral density. With regard to parametric approaches, different divergences are proposed in fitting a certain parametric family of spectral densities. Moreover, nonparametric approaches are also quite common considering the situation when we cannot specify the model of process. In this paper, we develop a local Whittle likelihood approach based on a general score function, with some special cases of which, the approach applies to more applications. This paper highlights the effective asymptotics of our general local Whittle estimator, and presents a comparison with other estimators. Additionally, for a special case, we construct the one-step ahead predictor based on the form of the score function. Subsequently, we show that it has a smaller prediction error than the classical exponentially weighted linear predictor. The provided numerical studies show some interesting features of our local Whittle estimator.     

General mixed Poisson regression models with varying dispersion

A general class of mixed Poisson regression models is introduced. This class is based on a mixing between the Poisson distribution and a distribution belonging to the exponential family. With this, we unified some overdispersed models which have been studied separately, such as negative binomial and Poisson inverse gaussian models. We consider a regression structure for both the mean and dispersion parameters of the mixed Poisson models, thus extending, and in some cases correcting, some previous models considered in the literature. An expectation–maximization (EM) algorithm is proposed for estimation of the parameters and some diagnostic measures, based on the EM algorithm, are considered. We also obtain an explicit expression for the observed information matrix. An empirical illustration is presented in order to show the performance of our class of mixed Poisson models. This paper contains a Supplementary Material.     

Review of the use of context in statistical image analysis

SUMMARY This paper is a review of the use of contextual information in statistical image analysis. After defining what we mean by 'context', we describe the Bayesian approach to high-level image analysis using deformable templates. We describe important aspects of work on character recognition and syntactic pattern recognition; in particular, aspects of the work which are relevant to scene understanding. We conclude with a review of some work on knowledge-based systems which use context to aid object recognition.     

ERROR BOUNDS FOR CALCULATION OF THE GITTINS INDICES

For a wide class of semi-Markov decision processes the optimal policies are expressible in terms of the Gittins indices, which have been found useful in sequential clinical trials and pharmaceutical research planning. In general, the indices can be approximated via calibration based on dynamic programming of finite horizon. This paper provides some results on the accuracy of such approximations, and, in particular, gives the error bounds for some well known processes (Bernoulli reward processes, normal reward processes and exponential target processes).