Wilcoxon–Mann–Whitney test for stratified samples and Efron's paradox dice

Two-treatment multi-center clinical trials are the most common type of clinical trials in practice. The aim of this paper is to discuss a curious property of certain standard nonparametric procedures used in the analysis of such clinical trials. Different analyses of a simulated data example are presented, which lead to contrasting and surprising results. The source of the potentially misleading outcome is then explored while relating the simulated data with the concept of Efron's paradox dice and the notion of nontransitivity. With the root of the problem established, an alternate nonparametric method from the literature is shown to address the problem. Finally, pointing out an interpretational concern of using the alternate procedure, a modification to this procedure is also suggested and corresponding theoretical results are presented.     

Generalized Laplacian approximations in Bayesian inference

This paper presents a new Laplacian approximation to the posterior density of η = g(θ). It has a simpler analytical form than that described by Leonard et al. (1989). The approximation derived by Leonard et al. requires a conditional information matrix R_η to be positive definite for every fixed η. However, in many cases, not all R_η are positive definite. In such cases, the computations of their approximations fail, since the approximation cannot be normalized. However, the new approximation may be modified so that the corresponding conditional information matrix can be made positive definite for every fixed η. In addition, a Bayesian procedure for contingency-table model checking is provided. An example of cross-classification between the educational level of a wife and fertility-planning status of couples is used for explanation. Various Laplacian approximations are computed and compared in this example and in an example of public school expenditures in the context of Bayesian analysis of the multiparameter Fisher-Behrens problem.     

The analysis of incomplete data using stochastic covariates

In the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV-1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour-bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumours.     

On the asymptotic normality of the L1- and L2-errors in histogram density estimation

The L₁ and L₂-errors of the histogram estimate of a density f from a sample X₁,X₂,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).     

孔子的学习思想综述

孔子首先是一个好学者,一个成功的学习者,而后才是一个成功的教育者。孔子的学习思想可以用“好学”来概括。孔子“好学”的精义在“求道”。孔子是渊博的学者、仁爱的教者和真诚的长者,是伟大的老师,善于将知识转化为魅力,善于引导人通过学习知识健康地成长。     

关于有效促进社会公正的几个问题

本文认为:(1)为了顺利地推进改革,为了中国社会经济持续、有效和健康的发展,就必须适应新的历史条件,顺应民意、顺应现代社会的基本趋势,把社会公正放到一个突出的位置。(2)在中国现阶段应当开始建立一个初级的社会公平保障体系。初级社会公平保障体系的基本特征是低水准、广覆盖、有实效。对于国家来说,近期需要做的事情可以分为两大块,一是国家的直接投入,二是国家的立法、监督、执行和引导。(3)有一些根深蒂固的观念在妨碍着我们重视社会公正问题。这些观念主要包括:“原始积累不可避免”,“国家财力不足”,“重视公正便会妨碍效率”,因此我们必须对这些观念进行一番必要的反思。(4)要想构建一个公正而和谐的社会,就必须培育一个庞大的中等收入者人群,形成一个“两头小,中间大”的橄榄型的社会结构,那么社会就会变得越来越稳定了。     

Two point priors and Γ-minimax estimating in families of uniform distributions

It is shown that when a parameter lying in a sufficiently small interval is to be estimated in a family of uniform distributions, a two point prior is least favourable under squared error loss. The unique Bayes estimator with respect to this prior is minimax. The Γ-minimax estimator is derived for sets Γ of priors consisting of all priors that give fixed probabilities to two specified subintervals of the parameter space if a two point prior is least favourable in Γ.     

凉山民族地区小学全科教师现状与培养途径

凉山民族地区是全国三大深度贫困地区,目前小学师资缺乏的问题普遍存在,进而造成小学全科教师师资不足在凉山民 族地区普遍存在。小学全科教师以跨学科教学为核心能力,而目前凉山民族地区的小学全科教师未达到这样的要求。凉山民 族地区小学全科教师应该是在掌握民族文化的基础上,以跨学科教学能力为核心,具有较好的实践教学能力,承担多门不同学 科课程的教学。凉山民族地区全科教师发展具有一定特殊性和历史性,针对其培养可以采用以公费师范生和普通小学全科教 师选拔培养为主要途径,结合本专科不同层级培养,加大现有凉山民族地区小学全科教师在职培训力度,最终实现凉山民族地 区小学全科教师专业素养达标。