Selection of certain dichotomous experiments

Summary The problem of allocating a single observation to one of the two available populations is considered. Suppose that a certain characteristic has densityf in one population, and has densityg in the other. On the basis of the value observed, one must specify which population has densityf. It is assumed that when a wrong population is chosen, a certain known loss is incurred. The problem is to allocate the observation so as to minimize the expected loss. General conditions onf andg are derived to decide which population should be selected for taking the observation. Research was supported in part by the National Science Foundation under grant No. SOC79-06386. Work done while on sabbatical leave at Carnegie-Mellon University.     

The asymptotic expansion as well as the exact moments of the stein estimator when the population means are nearly equal

Summary The purpose of this note is to derive the asymptotic distributions, means and variances of the Stein estimator, as well as that of the quadratic loss function for the vector case when the population means are nearly equal. These results are given in Section 3 and are obtained by using a method similar to the perturbation method, used by Nagao [4]. In Section 4 exact moments of the Stein estimator are also derived. Financially supported by the CSIR and the University of the OFS Research Fund.     

Estimation of the parameters of an exponential distribution under constrained location

In this paper, the problem of estimating parameters of an exponential population is studied under quadratic loss functions. The location parameter of the distribution is assumed to be bounded above by a known constant. Various classes of estimators are derived using integral expression of risk difference (IERD) method of Kubokawa (1994). Some complete class results are also established.     

Using simulation modelling for evaluating screening services for diabetic retinopathy

In using discrete event simulation for planning services in the health sector, epidemiologists and clinicians were closely involved in model design, data collection, analysis, validation and experimentation. For patients with diabetes, loss of sight can be prevented by timely treatment if detected sufficiently early. Simulation models, using the patient oriented simulation technique, POST, have been developed to assist policy makers in the choice of screening strategy in terms of operator, equipment, frequency of screening and target population. The models describe the progress of a population of diabetic patients, including new arrivals, over 25 years. The initial population were given characteristics retrospectively and the parameters were derived from peer reviewed publications. The results from the models show that the interval between screening is more important than screening sensitivity. The simulation can determine the expected workload and the amount of vision loss prevented for any population group.     

A bayes solution for the problem of ranking Poisson parameters

Summary It is desired to rank the parameters from a set of Poisson populations based on fixed, equal size samples from each population. A Bayes solution is derived for several types of loss functions and gamma priors, under the usual assumptions of symmetric and additive losses and symmetric priors. This research was sponsored by the office of Naval Research, Contract No. N000 14-68-A-0515, Project No. NR 042-260.     

Distribution of eigenvalues and eigenvectors of Wishart matrix when the population eigenvalues are infinitely dispersed and its application to minimax estimation of covariance matrix

We consider the asymptotic joint distribution of the eigenvalues and eigenvectors of Wishart matrix when the population eigenvalues become infinitely dispersed. We show that the normalized sample eigenvalues and the relevant elements of the sample eigenvectors are asymptotically all mutually independently distributed. The limiting distributions of the normalized sample eigenvalues are chi-squared distributions with varying degrees of freedom and the distribution of the relevant elements of the eigenvectors is the standard normal distribution. As an application of this result, we investigate tail minimaxity in the estimation of the population covariance matrix of Wishart distribution with respect to Stein's loss function and the quadratic loss function. Under mild regularity conditions, we show that the behavior of a broad class of tail minimax estimators is identical when the sample eigenvalues become infinitely dispersed.     

基于灰色预测模型的2008北京旅游人口预测分析

在分析北京市统计局2001至2006年入境旅游人口以及国内旅游人口统计数据的基础上,为研究每年同期旅游人数的变化规律,构造以每年3至12月的数据为分量的年数据向量.应用基于双谐样条插值算法对原异常数据进行处理,采用灰色预测模型及回归模型对2008北京旅游人口进行预测分析,得出2008年每月来京旅游人口数量,为政府制定人口相关政策提供参考.     

Dynamics of a reaction–diffusion–ODE system with quiescence

We consider a reaction–diffusion–ODE quiescent model in which the species can switch between mobile and immobile categories. We assume that the population inhabits a bounded region and study how its dynamics depend on the parameters describing switching rates and local population dynamics. Our results suggest that the transfer displays a stabilizing effect and inhibits the generation of spatial periodic solutions. A new method to obtain global stability and dissipative structure is also explored by constructing Lyapunov functionals to overcome the loss of compactness.     

Comparison of variance estimators for the ratio estimator based on small sample

1. Introduction and Main ResultsSuppose the population of interest consists of N distinct units labelled by 1,' f N.Associated with unit i are two values K and Xi, with Xi > 0 (i = 1,' t N). Denote thepopulation means of K and X, by Y and X respectively. To estimate Y, it is customaryto select a simple raPdom sample of size n and to use the ratio estimatNn = RX if Xis available, where R = y/x is an estimator for population ratio R = Y/X, y and x arerespectively the 8ample mean8 of…     

Optimal healthcare decisions: The importance of the covariates in cost-effectiveness analysis

This paper deals with the decision problem of choosing an optimal medical treatment, among M possible candidates, when the states of nature are the net benefit of the treatments, and regression models for the treatment cost and effectiveness are assumed. In this setting a crucial step in the analysis is the construction of the population subgroups sharing characteristics specified by the covariates, so that optimal decisions are now not for the whole population of patients but for patient population subgroups.We argue that the existing formulations of population subgroups in the literature are too rigid and unrealistic for real applications, and instead we formulate the population subgroups on the base of selected “influential” covariates. The Bayesian variable selector we use is an optimal one under the 0-1 loss function, which means choosing the subset of covariates having the highest posterior probabilities based on the so-called intrinsic priors, an objective Bayesian tool that exhibits an excellent performance.For each population subgroup we study the optimal Bayesian decisions for two different utility functions. One optimal decision is that obtained maximizing the expected net benefit, and the other maximizing the expected number of times that the treatment having the highest net benefit is chosen.Illustrations of the procedure for real data show that the subset of influential covariates may vary across treatments. Subgroup optimal treatments are derived and compared with those given by preceding methods.     

The sample mean as an estimator of the location parameter in the case of a Laplacian loss function and a nuisance scale parameter

Under certain a priori conditions it is shown that the sample mean is an admissible estimator of the location parameter in the case of a Laplacian loss function and a nuisance scale parameter only for samples from a Gaussian population.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 43, pp. 15–29, 1974.     

关于经验分布的最优选择问题

本文运用统计决策知识探索了经验分布的最优选择问题. 作者借鉴风险函数的思想, 在平方损失的意义下引进平均平方距离标准, 并推导出该标准下最优新经验分布函数. 继而采用另一源于Minimax思想的最大一次距离标准, 在连续总体下对五种经验分布函数加以模拟比较分析, 得出新经验分布函数仍一致占优.     

平衡损失下有限总体回归系数的线性可容许预测

本文研究了平衡损失函数下正态总体和非正态总体中有限回归系数的可容许预测.利用统计决策理论,获得了非正态总体中齐次线性预测为可容许预测的充分必要条件和在正态总体中齐次线性预测在一切预测类中可容许性的充要条件,推广了二次损失下的若干相关结果.     

Linear Minimax Prediction in a Finite Population with Ellipsoidal Constraints

Under a matrix loss function, we investigate the prediction problem in a finite population with ellipsoidal restriction in this paper. Firstly, a class of homogeneous linear minimax predictors for finite population regression coefficient are obtained. Moreover, it is shown that the linear minimax predictors are admissible in the class of homogeneous linear predictors. Finally, a simulation study and a real data example are used to illustrate our results.     

A multi-agent model describing self-renewal of differentiation effects on the blood cell population

In this work, a new multi-agent model is used to describe blood cell population dynamics. More particularly, we focus our simulations here on differentiation and self-renewal process based on cell communication. We consider the different cases where progenitor cells are able to self-renew or not in the bone marrow. As a consequence of this study, we give some possible explanations of the mechanism for recovery of the system under important blood loss or blood diseases such as anemia.     

On estimating domain totals over a subpopulation

A simple random sample is drawn over a finite population which is composed of several subpopulations. Each subpopulation consists several domains. The minimax estimator under squared error loss function for the domain totals over a subpopulation is derived, in which the number of sample units falling into the subpopulation is random.Supported by the General Research Fund of the University of Kansas.     

Enhanced annuities and the impact of individual underwriting on an insurer’s profit situation

We analyze the effect of enhanced annuities on an insurer engaging in individual underwriting. We use a frailty model for heterogeneity of the insured population and model individual underwriting by a random variable that positively correlates with the corresponding frailty factor. For a given annuity portfolio, we analyze the effect of the quality of the underwriting on the insurer’s profit/loss situation and the impact of adverse selection effects.     

Estimation of two normal means which may be common

Consider the problem of estimating the mean of a normal population when independent samples from this as well as a second normal population are available. Pre-test estimators which combine the two sample means if a test of the hypothesis of equal population means accepts but otherwise use only the first sample mean, are compared to limited translation estimators which are derived in the spirit of Bickel (1984, Ann. Statist., 12, 864–879) (we also cover the cases of unknown variances). Our conclusion is that if the accuracy with which the second population mean can be estimated is of the same or better order of magnitude as teh accuracy with which the first can be estimated, then the limited translation estimators largely dominate the pre-test estimators in terms of mean square error loss.This research was supported by grants from the FRD of the CSIR of South Africa.     

A note on accelerated sequential estimation of the mean of NEF-PVF distributions

The minimum risk point estimation for the mean is addressed for a natural exponential family (NEF) that also has a power variance function (PVF) under a loss function given by the squared error plus linear cost. An appropriate accelerated version of the full purely sequential methodology of Bose and Boukai (1993b, submitted) is proposed along the lines of Mukhopadhyay (1993a, Tech. Report, No. 93-27, Department of Statistics, University of Connecticut) in order to achieve operational savings. The main result provides the asymptotic second-order expansion of the regret function associated with the accelerated sequential estimator of the population mean.     

总人口规模变化的年龄结构MSEIR流行病模型的再生数

在总人口规模变化和疾病影响死亡率的假设下,讨论了带二次感染和接种疫苗的年龄结构MSEIR流行病模型.首先给出再生数R(ψ,λ)(这里ψ(a)是接种疫苗率,λ是总人口的增长指数)的显式表达式.其次,证明了当R(ψ,λ)<1时,系统的无病平衡态是稳定的;当R(ψ,λ)>1时,无病平衡态是不稳定的.