正态总体方差和标准差的无偏估计

在正态总体分布下,给出了方差及标准差的矩估计量和极大似然估计量,讨论了两者之间的关系,得出两类估计量相同,并进一步给出无偏估计量。     

正态分布中参数的自助法稳健估计

通过四分数构造的位置参数与尺度参数的自助法稳健估计量来估计正态分布的参数，这些估计量的精确性通过重复抽样计算得到的MSE与偏差来衡量．通过基于污染数据与未污染数据对应参数的自助法稳健估计量与传统估计量的数值比较，验证新构建估计量的稳健性。     

一种Archimedean copula函数模型选择的新方法

首先证明样本Kendall秩相关系数■是总体Kendall秩相关系数τ的一致估计量,且样本Spearman秩相关系数■是总体Spearman秩相关系数ρ_s的一致估计量.其次,在■、■这两个一致估计量的基础上,构建了一种新的一致估计量.实证分析表明,基于新的一致估计量的函数选择模型较原来方法有较大的改进.     

基于捕获-再捕获模型的双系统估计量模型式框架

用来估计人口总体真实人口数目的双系统估计量建立在捕获一再捕获模型基础上．这里的双系统指构造的估计量要同时用到普查资料系统和再普查资料系统．双系统估计量有I型和Ⅱ型2种形式．I型双系统估计量是其基本形式,构造较为简单．Ⅱ型双系统估计量充分考虑了普查与再普查之间发生的人口迁移,构造比较复杂,是其高级形式．     

基于截尾数据的极值分布参数的简单估计量

本介绍了极值分布参数的新的估计量，对截尾少于20％（0．8≤P＜1．0）的情况，新估计量显示出比原先提出的估计量有更高的效率，本对新估计量的一优势作了分析，并找出了一这优势存在的原因，由此说明通过新估计量可进行显检验和计算置信区间。     

回归模型中异方差的检验方法

异方差的存在并不破坏普通最小二乘法估计量的无偏性,但是估计量的方差变大了,由于估计量方差的变大,就使通常假设检验的值不可靠,因此选取适当的异方差的检验方法是极其重要的.     

用修正系数法构造θ~2的无偏估计

在总体分布为指数分布和均匀分布时,由未知参数θ的无偏估计量,通过修正系数法直接构造θ2的无偏估计量.     

回归模型中异方差的检验方法

异方差的存在并不破坏普通最小二乘法估计量的无偏性，但是估计量的方差变大了，由于估计量方差的变大，就使通常假设检验的值不可靠，因此选取适当的异方差的检验方法是极其重要的．     

关于Γ-分布参数的估计量

本文给出了Г-分布G（α,β）参数α的修正矩法估计量和参数β的修正极大似然估计量,并证明了它们具有无偏性和强相合性．     

基于均匀核的柯西密度估计

非参数核密度估计具有良好的性质,有固定窗宽和变窗宽两种形式,由于渐近方差收敛率相同,而渐近偏度存在差异,固定窗宽和球估计量的偏度为h2,Ambramson估计量为h4,本文提出了固定窗宽核密度估计量的一个性质,并计算基于均匀核的柯西密度Ambramson估计量的期望发现刚好是无偏的。     

一类指数分布族的参数估计问题

考虑了一类单参数指数族分布的估计问题,在熵损失下讨论了此类分布中未知参数的Bayes估计，给出了未知参数的一个无偏估计并验证了此估计量所具有的一些优良性质,最后在对称熵损失下得出了所讨论参数的Bayes估计。     

参数的广义矩法估计

对参数的矩法估计是一个基本方法,它首先要求随机变量的矩存在;但是对某些分布,它不存在矩,因此,对该分布参数的估计矩法将失效。本文提出广义矩概念,并给出了广义矩存在的条件,利用广义矩对参数作出估计,弥补了不存在短或矩的阶不够大时导致参数估计矩法失效的不足。     

Strong Convergence of the Coefficient Alpha Estimator for Reliability of Multiple-Component Measuring Instruments

It is shown that in general the popular coefficient alpha estimator for reliability of multi-component measuring instruments converges almost surely to a quantity that is not equal to the population reliability coefficient. This convergence with probability 1 is a stronger statement than convergence in probability (consistency) and convergence in distribution for the alpha estimator, which have been studied in the past. In the special case of congeneric measures with uncorrelated errors and equal loadings on the common true score, the alpha estimator converges almost surely to the population reliability coefficient that equals population alpha, which implies also its consistency as a reliability estimator. When the loadings are unequal but sufficiently high and similar, the alpha estimator converges almost surely to population alpha that is essentially indistinguishable from the population reliability coefficient, which implies alpha’s approximate consistency then. For the general case, the results entail that the alpha estimator is not a consistent estimator of reliability. The findings add to the critical literature on coefficient alpha in the general case, as well as to the justification of its use as a dependable measuring instrument reliability estimator in special cases and settings resulting under appropriate restrictive conditions, and are illustrated using a numerical example.     

线性混合效应模型中方差分量两种估计的比较

本文首先给出了由王松桂等提出的广义谱分解估计(GSDE)的定义,以及由Herderson方法得到的方差分量的方差分析估计(ANOVAE),在此基础上提出了谱和线性混合效应模型的概念,证明了在这类模型中,方差分析估计是广义谱分解估计的一种,并且考察了在一定条件下广义谱分解估计优于方差分析估计的充分条件.     

Improved estimator of the continuous-time kernel estimator

There have been many papers presenting kernel density estimators for a strictly stationary continuous time process observed over the time interval [0, T ]. However the estimators do not satisfy the property of mean-square continuity if the process is mean-square continuous. In this paper we present a modified kernel estimator and substantiate that the modified estimator satisfies the property of mean-square continuity. In a simulation study the results show the modified estimator is better than the original estimator in some cases.     

时间序列中一种模型的最优预测的研究

给出一种新的带有有色噪声模型,这种新的模型通过转换,应用现代时间序列分析方法,基于ARMA信息模型和白噪声估值器,求出状态的非递推估值器,最后得到新模型统一的、稳态的Kalman估值器．     

Strong Consistency of Reliability Estimators for Multiple-Component Measuring Instruments

It is shown that the maximum likelihood estimator of the widely used omega coefficient for reliability of multicomponent measuring instruments converges almost surely to the population reliability coefficient for normal congeneric measures with uncorrelated errors as sample size increases indefinitely. This strong consistency implies convergence in probability (consistency) as well as in distribution for the omega estimator. Strong consistency is also demonstrated for the maximal reliability estimator associated with the optimal linear combination of the instrument components. The findings of this note add (i) to the recommendation to use in the general normality case the omega estimator in empirical research, (ii) to the critical literature on the popular coefficient alpha then, and (iii) to the literature on the properties of the optimal linear combination of observed measures and the maximal reliability estimator.     

约束线性模型下回归系数的条件根方估计

本文提出了约束线性模型下回归系统的条件根方估计和广义条件根方估计,证明了在一定的条件下,两者在均方误差意义都能很好地改进回归系数的约束最小二乘估计,并讨论了它们的可容许性及广义条件根方估计中未知参数的选取方法。     

Applying the Liu-Agresti Estimator of the Cumulative Common Odds Ratio to DIF Detection in Polytomous Items

Liu and Agresti (1996) proposed a Mantel and Haenszel-type (1959) estimator of a common odds ratio for several 2 × J tables, where the J columns are ordinal levels of a response variable. This article applies the Liu-Agresti estimator to the case of assessing differential item functioning (DIF) in items having an ordinal response variable. A simulation study was conducted to investigate the accuracy of the Liu-Agresti estimator in relation to other statistical DIF detection procedures. The results of the simulation study indicate that the Liu-Agresti estimator is a viable alternative to other DIF detection statistics.