Protection against outliers in empirical bayes estimation

The proven optimality properties of empirical Bayes estimators and their documented successful performance in practice have made them popular. Although many statisticians have used these estimators since the landmark paper of James and Stein (1961), relatively few have proposed techniques for protecting them from the effects of outlying observations or outlying parameters. One notable series of studies in protection against outlying parameters was conducted by Efron and Morris (1971, 1972, 1975). In the fully Bayesian case, a general discussion on robust procedures can be found in Berger (1984, 1985). Here we implement and evaluate a different approach for outlier protection in a random-effects model which is based on appropriate specification of the prior distribution. When unusual parameters are present, we estimate the prior as a step function, as suggested by Laird and Louis (1987). This procedure is evaluated empirically, using a number of simulated data sets to compare the effects of the step-function prior with those of the normal and Laplace priors on the prediction of small-area proportions.     

New Approaches in Risk Assessment for Carcinogens

Methods are needed to improve the ability of biomonitoring and epidemiological studies to identify potential carcinogenic hazards and to quantify human risk. The limitations of pharmacokinetic models can be mitigated by the direct measurement of molecular markers of biologically effective dose of carcinogen. Parallel animal and human studies are recommended as a means of validating these markers.     

ON THE HILDRETH-HOUCK ESTIMATOR FOR RANDOM COEFFICIENT REGRESSION MODELS

This paper is concerned with the linear regression model in which the coefficients are random variables. The Hildreth-Houck method is considered for estimating the model. Sufficient conditions for the consistency of the Hildreth-Houck estimator are discussed and its asymptotic normality is established.     

An Evaluation of the Rai and Van Ryzin Dose-Response Model in Teratology

The underlying assumptions of the Rai and Van Ryzin dose-response model for reproductive toxicological data are evaluated on the basis of existing experimental data. The model under consideration is unusual in its use of litter size to completely account for extra-binomial variation in the data by associating litter size with reproductive outcome. The experimental data show that controlling litter size is not sufficient to account for the litter-to-litter variability in responses. It is also shown that the two linear components of the Rai and Van Ryzin model are inappropriate. For the component which applies to the dam, the data suggest a strong nonlinearity, supported by rejection of the linear model via statistical hypothesis tests. In the component involving litter size, a relationship with dose is not apparent. The litter size parameters offer considerable potential for bias in estimation; bias which is at least partly masked by the model having good prediction characteristics due to the increased number of parameters. A simulation study is presented to illustrate how the Rai and Van Ryzin model can exaggerate litter size effects on the probability of response when the simulated data arise from a model involving a nonlinear dam component, common to this type of data, and no effect of litter size.     

我国工科数学改革模式的探索

分析我国工科数学改革历史与现状,论述改革的必要性与紧迫性,提出改革的基本思路。     

An EM-type algorithm for multivariate mixture models

This paper introduces a new approach, based on dependent univariate GLMs, for fitting multivariate mixture models. This approach is a multivariate generalization of the method for univariate mixtures presented by Hinde (1982). Its accuracy and efficiency are compared with direct maximization of the log-likelihood. Using a simulation study, we also compare the efficiency of Monte Carlo and Gaussian quadrature methods for approximating the mixture distribution. The new approach with Gaussian quadrature outperforms the alternative methods considered. The work is motivated by the multivariate mixture models which have been proposed for modelling changes of employment states at an individual level. Similar formulations are of interest for modelling movement between other social and economic states and multivariate mixture models also occur in biostatistics and epidemiology.     

目标规划在国外高校管理中应用的一个实例

本文介绍国外一高校利用目标规划模型辅助院长制定人力资源计划、争取经费、辅助决策的应用情况。     

平坝区D优63高产栽培综合农艺措施研究

采用五元二次正交旋转组合设计方法,在影响杂交水稻 D 优63产量的诸因素中,选择了五项主要因素,建立五元二次回归模型,在此基础上经电子计算机模拟、筛选,提出 D 优63在平坝区种植条件下,对产量影响较大的因素是秧龄和基本苗,其次是施磷量和施钾量。同时明确了不同产量水平的农艺措施配套方案。     

On the identification of ARMA echelon-form models

An identification procedure for multivariate autoregressive moving average (ARMA) echelon-form models is proposed. It is based on the study of the linear dependence between rows of the Hankel matrix of serial correlations. To that end, we define a statistical test for checking the linear dependence between vectors of serial correlations. It is shown that the test statistic t?_n considered is distributed asymptotically as a finite linear combination of independent chi-square random variables with one degree of freedom under the null hypothesis, whereas under the alternative hypothesis, t?_N/N converges in probability to a positive constant. These results allow us, in particular, to compute the asymptotic probability of making a specification error with the proposed procedure. Links to other methods based on the application of canonical analysis are discussed. A simulation experiment was done in order to study the performance of the procedure. It is seen that the graphical representation of t?_N, as a function of N, can be very useful in identifying the dynamic structure of ARMA models. Furthermore, for the model considered, the proposed identification procedure performs very well for series of 100 observations or more and reasonably well with short series of 50 observations.     

ASYMPTOTIC PROPERTIES OF RESTRICTED MAXIMUM LIKELIHOOD (REML) ESTIMATES FOR HIERARCHICAL MIXED LINEAR MODELS

This paper explores the asymptotic distribution of the restricted maximum likelihood estimator of the variance components in a general mixed model. Restricting attention to hierarchical models, central limit theorems are obtained using elementary arguments with only mild conditions on the covariates in the fixed part of the model and without having to assume that the data are either normally or spherically symmetrically distributed. Further, the REML and maximum likelihood estimators are shown to be asymptotically equivalent in this general framework, and the asymptotic distribution of the weighted least squares estimator (based on the REML estimator) of the fixed effect parameters is derived.