最大熵先验下的正态分布总体的Bayes分析

在正态分布总体方差已知时,满足总体均值为正,且其期望为某常数的约束条件下,应用最大熵原理获取先验分布,并求得后验分布.利用该后验分布得出总体期望的Bayes估计及可信区间.解决了经典统计中难以解决的问题.最后用算例说明其应用.     

非平衡随机效应模型中方差分量的经验Bayes检验

本文研究了非平衡随机效应模型中方差分量的经验Bayes 检验问题. 利用多元密度函数核估计方法构造了参数的经验Bayes(EB)判决函数,证明了该判决函数的渐近最优性,得到了其收敛速度,并给出了一个满足本文结论条件的先验分布.     

一类相合的分位点型检验

广义非参数似然比检验统计量是一类很广的统计量,包含了众多重要的检验统计量,如Anderson-Darling(AD)等.利用Rubin的随机经验分布函数替代经验分布函数的方法,得到了广义非参数似然比检验统计量的新版本,构造了新的检验统计量.由于新的检验统计量在给定样本下仍然是随机变量,选择了它的分位点和期望作为检验统计量,分别称之为分位点型检验统计量和期望型检验统计量.在简单假设情况下,证明了分位点型检验统计量和期望型检验统计量在固定备择下的相合性.模拟结果显示,在某些备择下,新的检验的功效明显高于原有的基于经验分布函数的检验的功效.     

统计学入门(Ⅻ)

二十四、其它常用的非参数检验方法 §24-1非参数检验的特点 我们已经讨论过许多检验方法。这些方法可以分成两类;一类是已知总体的分布类型(例如正态分布或二项分布等),检验的原假设是关于总体分布参数的,这种检验通常称为参数检验;另一类是不对总体分布作任何事先的假定,而检验的原假设是关于总体分布类型本身(例如x2拟合优度检验)或其它我们感兴趣的形式(例如列联表中的变量独立性检验),这些假设都不是表示成分布参数形式的,因此称为非参数检验。 对总体分布不需要加以限制,其方法可适用于任何分布,是非参数检验的最突出的优点。非参数检…     

定数截尾两参数指数——威布尔分布形状参数的Bayes估计

在不同的损失函数下,本文研究了两参数指数—威布尔分布(EWD)形状参数的Bayes估计问题.基于定数截尾试验,当其中一个形状参数α已知时,给出了另一个形状参数θ在三种不同损失函数下的Bayes估计表达式,并求得了可靠度函数的Bayes点估计.最后运用随机模拟方法,将Bayes估计和极大似然估计进行了比较.结果表明,LINEX损失下Bayes估计的精度比极大似然估计高.     

基于随机加权的空间聚集性检验及其在基础教育师资均衡性评价中的应用

使用空间统计检验方法研究北京基础教育资源分配的均衡性问题.对于空间分布均匀性的检验,常用的统计量是Moran's I统计量.但基于Moran's I统计量做推断的时候,人们往往用渐进正态分布或者用Bootstrap反复抽样得到经验分布来进行.提出使用随机加权法进行统计量的经验检验.Jin和Lee(2014)文中得出基于Bootstrap的Moran's I统计量满足一致逼近和渐进正态等性质.采用类似的统计工具证明了基于随机加权得到的统计量的渐进分布也满足这些良好性质.填补了用随机加权法在空间统计量的推断中理论保证的空白.通过模拟研究,证明了所提算法的有效性.方法应用于北京基础教育的师资-适龄儿童数比例,师资-在校生数比例的空间聚集性检验中得到了良好的应用,并与其它检验方法所得结论进行比较.结论显示在不同相邻概念(地理相邻、政策空间相邻)下,方法得到的结论符合常理.     

对数正态分布场合下产品加固性能的Bayes评估方法

总结了评估产品抗辐射能力实验中常常遇到的三类数据.针对产品抗辐射能力服从对数正态分布、实验样本数据为成败型实验数据的情形,运用Bayes方法给出了在小样本情况下,产品平均抗辐射能力大于给定指标要求的后验概率的计算方法以及在给定置信度下产品平均抗辐射能力置信下限的计算方法.讨论了未知参数先验分布的确定方法, 并给出了评估方法的具体例子.     

测量误差为Laplace分布的非线性统计推断

当p-维参数θ通过矩条件Em(X,θ)=0定义,且X带有Laplace测量误差时,即我们只能观测到Z=X+U,文献中提出了一种基于无条件期望关系Em(X,θ)=EH(Z,θ)的估计方法,其中H为某个形式已知的函数.然而该方法仅适用于U的各分量服从Laplace分布且相互独立的情况.文章将介绍一种一般的多元Laplace分布,并将基于无条件期望的估计方法推广到具有这种多元Laplace分布的测量误差模型中.另外,基于无条件期望关系的估计方法对一些统计推断问题并不适用.文章将构造一种基于条件期望E[m(X,θ)|Z]的估计方法.当X为一维时,我们对这些估计的大样本性质进行了讨论.     

具有Rao简单结构的多元t-模型的参数区间估计

在统计推断中,模型中未知参数的区间估计是一个重要的研究内容.本文通过构造枢轴量研究了具有Rao简单结构多元￡-模型的参数区间估计,利用条件分布技巧,得到枢轴量的分布,从而获得模型中单个未知参数的置信区域以及参数的联合置信区域.     

多元Cp值

本文给出了多元工序能力指数C_p的定义,有关分布,置信下限和判断工序是否有能力的临界值,可用来对多质量特性工序能力作统计推断。     

Randomized statistical inference: A unified statistical inference frame of frequentist,fiducial, and Bayesian inference

We propose randomized inference(RI), a new statistical inference approach. RI may be realized through a randomized estimate(RE) of a parameter vector, which is a random vector that takes values in the parameter space with a probability density function(PDF) that depends on the sample or sufficient statistics,such as the posterior distributions in Bayesian inference. Based on the PDF of an RE of an unknown parameter,we propose a framework for both the vertical density representation(VDR) test and the construction of a confidence region. This approach is explained with the aid of examples. For the equality hypothesis of multiple normal means without the condition of variance homogeneity, we present an exact VDR test, which is shown as an extension of one-way analysis of variance(ANOVA). In the case of two populations, the PDF of the Welch statistics is given by using the RE. Furthermore, through simulations, we show that the empirical distribution function, the approximated t, and the RE distribution function of Welch statistics are almost equal. The VDR test of the homogeneity of variance is shown to be more efficient than both the Bartlett test and the revised Bartlett test. Finally, we discuss the prospects of RI.     

多个正态总体均值相等的VDR检验

本文将随机估计由一维参数扩展至多维参数,基于随机估计的密度函数提出VDR检验.在总体方差已知和未知的两种情形下,本文讨论多个正态总体均值是否相同的VDR检验过程,而且得到精确的检验.单因素方差分析是VDR检验的特例.模拟研究表明,VDR检验是一个普遍适用的方法.     

Fiducial inference in the pivotal family of distributions

In this paper a family, called the pivotal family, of distributions is considered. A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is given. The method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.     

位置参数分布族中Fiducial分布与后验分布的关系

本文考虑本质位置参数分布族中,参数的Fiducial分布与后验分布的等同问题．首先讨论了如何给出Fiducial分布,分析结果表明以分布函数形式给出Fiducial分布要比密度函数形式合理,同时,证明了所给的Fiducial分布具有频率性质．然后,研究在参数受到单侧限制时,Fiducial分布与后验分布等同的问题,给出的充要条件是分布族为指数分布族,此时,先验分布是一个广义先验分布,它不能被Lebesgue测度控制．最后,证明了在参数限制在一个有限区间内时,Fiducial分布与任何先验(包括广义先验分布)下的后验分布不等同．     

Finite-sample inference with monotone incomplete multivariate normal data, I

We consider problems in finite-sample inference with two-step, monotone incomplete data drawn from , a multivariate normal population with mean and covariance matrix . We derive a stochastic representation for the exact distribution of , the maximum likelihood estimator of . We obtain ellipsoidal confidence regions for through T², a generalization of Hotelling’s statistic. We derive the asymptotic distribution of, and probability inequalities for, T² under various assumptions on the sizes of the complete and incomplete samples. Further, we establish an upper bound for the supremum distance between the probability density functions of and , a normal approximation to .     

New estimating equation approaches with application in lifetime data analysis

Estimating equation approaches have been widely used in statistics inference. Important examples of estimating equations are the likelihood equations. Since its introduction by Sir R. A. Fisher almost a century ago, maximum likelihood estimation (MLE) is still the most popular estimation method used for fitting probability distribution to data, including fitting lifetime distributions with censored data. However, MLE may produce substantial bias and even fail to obtain valid confidence intervals when data size is not large enough or there is censoring data. In this paper, based on nonlinear combinations of order statistics, we propose new estimation equation approaches for a class of probability distributions, which are particularly effective for skewed distributions with small sample sizes and censored data. The proposed approaches may possess a number of attractive properties such as consistency, sufficiency and uniqueness. Asymptotic normality of these new estimators is derived. The construction of new estimation equations and their numerical performance under different censored schemes are detailed via Weibull distribution and generalized exponential distribution.     

The admissibility of the empirical mean location for the matrix von Mises–Fisher family

In this note we consider von Mises–Fisher families of probability densities on spheres and more generally on Stiefel manifolds, which include the orthogonal groups. It addresses the estimation of the mean direction or the mean location by empirical mean location, which for the von Mises–Fisher family coincides with the maximum likelihood estimator. It is shown that (with a few exceptions) the empirical mean location of a sample is almost surely uniquely defined and that it is unbiased in the sense that its mean location coincides with the mean location of the von Mises–Fisher distribution. The main goal, however, is to show that empirical mean location is an admissible estimator for the mean location of the von Mises–Fisher distribution.     

Heavy tailed capital incomes: Zenga index,statistical inference,and ECHP data analysis

Micro-data of European Union (EU) countries show that capital incomes account for a large part of disparity in populations and follow heavy-tailed distributions in many EU countries. Measuring and comparing the disparity requires incorporating the relative nature of ‘small’ and ‘large,’ and for this reason we employ the newly developed Zenga index of economic inequality. Its non-parametric estimator does not fall into any well known class of statistics. This makes the development of statistical inference a challenge even for light-tailed populations, let alone heavy-tailed ones, as is the case with capital incomes. In this paper we construct a heavy-tailed Zenga estimator, establish its asymptotic distribution, and derive confidence intervals. We explore the performance of the confidence intervals in a simulation study and draw conclusions about capital incomes in EU countries, based on the 2001 wave of the European Community Household Panel (ECHP) survey.     

Sensitivity of Bayes decisions for the success probability for samples from a nonbinomial population

Summary A family of generalised negative binomial distributions is employed to investigate inference robustness of the Bayes estimator of the unknown parameter of the binomial distribution. A zone of sensitivity for the test of significance is constructed to forewarn the pro-Jeffreys Bayesians against indiscriminate choice of the probability in favour of the null hypothesis. A few selected tables are presented to illustrate the effect of relaxation of the ‘binomiality’ assumption.     

基于混合Ⅰ型删失数据的威布尔模型精确推断（英文）

威布尔分布是可靠性和寿命测试试验中常用的模型.本文中,我们考虑了基于混合Ⅰ型删失数据的威布尔模型精确推断.我们得到了威布尔分布未知参数最大似然估计的精确分布以及基于精确分布的置信区间.由于精确分布函数较为复杂,我们也给出了未知参数的另外几种置信区间,比如,基于近似方法的置信区间,Bootstrap置信区间.为了评价本文的方法,我们给出了一些数值模拟的结果.