有辅助信息时有限总体分布函数的新估计量

本文提出两个新的估计量,利用观察数据中的总体辅助信息来估计有限总体分布函数,并通过两个人工总体的模拟实验,比较新的估计量、传统的估计量及Rao,Kover&Mantel(1990)提出的估计量的相对平均误差与相对标准差。结果表明,从相对标准差的角度分析,两个新的估计量有一个是四个估计量中精度最好的一个,另一个也有很好的表现;而且它们在模型有所偏差时都具备了较好的稳健性。     

为PPS抽样而进行双重抽样的方法

本文把双重抽样技术用于ＰＰＳ抽样，给出了该方法下总体总值的无偏估计量，估计量的方差及方差的无偏估计公式。     

论双系统估计量的无偏性

人口普查质量评估中所使用的双系统估计量是否为无偏估计量是一个很值得深入讨论的问题。只有无偏,才能确保使用双系统估计量估计的目标总体实际人数及人口普查净误差平均等于它们的实际数。针对人口普查质量评估工作中所使用的双系统估计量,论证这个估计量的无偏性条件。采用从既定假设出发进行推演的路径论证。研究结果表明,双系统估计量是目标总体实际人数无偏估计量的必要但非充分的条件是,人口普查与其质量评估调查相互独立以及目标总体中的每一个人在人口普查中的登记概率相同,在质量评估调查中登记的概率也相同。     

关于无偏估计的几个问题

估计量的无偏性概念是频率学派思想的充分体现,它只有在大量重复使用估计量时才有意义.简单性和绝对化地使用无偏性是不合理的.实例显示无偏估计有时并不一定存在,可估参数的无偏估计往往不唯一,无偏估计不一定是好估计.     

利用样本分位数的Logistic总体分布参数的近似最佳线性无偏估计

Harter H_L.,Balakrishnan N.等先后讨论了Logistic总体分布参数的极大似然估计,近似极大似然估计;其后Ogawa J.,Lloyd E.H.,Kulldorff G.,Gupta S.S,及chan L.K. 等又先后讨论了Logistlic分布参数的最佳线性无偏估计及估计的相对效率等问题.令人遗憾的是:在大样本情形下,上述估计均难以求得.为缓解这一困难,本文讨论利用样本分位数的Logistic总体的近似最佳线性无偏估计,给出估计量的大样本性质,以及样本分位数不超过10情形下,估计量有渐近最大相对估计效率时样本分位数的选取方案等.     

基于s估计σ引出的无偏修正

用s去估计总体分布的标准差σ不是无偏估计,在特定总体分布下,可以通过简单的修正达到无偏估计.修正系数的确定与样本容量有关.     

过程能力指数评价过程能力的可靠性影响因素分析

利用过程能力指数评价过程能力,其可靠性程度会受到抽样误差、测量误差以及数据自相关性的影响,分析了观测数据受各种因素影响下过程能力指数估计的统计性质,给出了通过添加纠偏系数获得过程能力指数无偏估计或无偏估计近似值的方法。     

在几种常见的抽样方案下的事后分层

本文给出系统抽样，放回不等概率抽样及二阶不等概率抽样情况下总体均值的事后分层估计，估计量的方差和它的无偏估计。     

二元Kundu-Gupta型二点分布参数的最大似然估计

讨论二元Kundu-Gupta型二点分布的识别性及参数估计,已知可识最小值的分布时,则参数可识别;由此得到了参数的最大似然估计;其中二个参数的估计量是无偏的,另外一个参数的估计量的期望不存在;模拟结果显示:估计值均稳定于真值参数.     

均匀分布参数的无偏估计及其分布

讨论了均匀分布未知参数无偏估计量的分布密度,利用无偏估计量构造出一些新的样本函数,并且利用给出的样本函数推导出了未知参数的置信区间.所得到结果改善了现有的估计,易于计算.     

纵向数据下半参数回归模型估计的收敛速度

考虑纵向数据下半参数回归模型:yij=x′ijβ+g(tij)+eij,i=1,…,n,j=1,…,mi.基于最小二乘法和一般的非参数权函数方法给出了模型中参数β和回归函数g(·)的估计,并在适当条件下证明了参数分量β的估计量的强收敛速度和未知函数g(·)的估计量的一致强收敛速度.     

IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.     

Orthogonally invariant estimation of the skew-symmetric normal mean matrix

The unbiased estimator of risk of the orthogonally invariant estimator of the skew-symmetric normal mean matrix is obtained, and a class of minimax estimators and their order-preserving modification are proposed. The estimators have applications in paired comparisons model. A Monte Carlo study to compare the risks of the estimators is given.     

On Bayes and unbiased estimators of loss

We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In 3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988, On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly, that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss. Research supported by NSF Grant DMS-97-04524.     

方差分量的二次不变估计的非负改进

研究一类方差分量模型中的方差分量的估计改进问题,首先在含两个方差分量模型中给出σ21二次型估计类,并且此估计类还具有无偏性和不变性.考虑二次损失(δ-θ)2,在此估计类基础上放弃无偏性进行非负改进,不仅得到优于二次不变无偏估计类的σ21的非负二次不变估计类,而且还说明了它优于方差分析估计和最小均方误差估计,文献[5]中给出s>2时的非负改进,但是非负改进存在是有条件的,本文克服了这个缺陷.最后给出了非负改进存在的充分必要条件.     

Superiority of empirical Bayes estimator of the mean vector in multivariate normal distribution

In this paper, the Bayes estimator and the parametric empirical Bayes estimator (PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator (MVUE) and a revised James-Stein estimators (RJSE) are investigated respectively under mean square error (MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion.     

Classroom note: Estimation of the cross-product of two mean vectors

The problem of estimating the cross-product of two mean vectors in three-dimensional Euclidian space is considered. Two ‘natural’ estimators are developed, both of which turn out to be biased. A third, unbiased estimator, resulting from a jackknife procedure, is also investigated. It is shown that, under normality, the latter is best among all the unbiased estimators of this quantity.     

受约束回归模型参数的统一几乎无偏估计

考虑实际回归问题中存在更多受约束条件的情况,提出了带约束的统一几乎无偏估计类,统一了常见的具有线性约束的回归模型的几乎无偏估计,进一步的研究给出了在均方误差和均方误差矩阵意义下,带约束的统一几乎无偏估计优于一般带约束的最小二乘估计的充分条件和椭球范围.     

Asymptotic Comparisons of Several Variance Estimators and their Effects for Studentizations

In this paper we obtain asymptotic representations of several variance estimators of U-statistics and study their effects for studentizations via Edgeworth expansions. Jackknife, unbiased and Sen's variance estimators are investigated up to the order o^p(n^-1). Substituting these estimators to studentized U-statistics, the Edgeworth expansions with remainder term o(n^-1) are established and inverting the expansions, the effects on confidence intervals are discussed theoretically. We also show that Hinkley's corrected jackknife variance estimator is asymptotically equivalent to the unbiased variance estimator up to the order o^p(n^-1).     

Asymptotic Analysis of the Jittering Kernel Density Estimator

Jittering estimators are nonparametric function estimators for mixed data. They extend arbitrary estimators from the continuous setting by adding random noise to discrete variables. We give an in-depth analysis of the jittering kernel density estimator, which reveals several appealing properties. The estimator is strongly consistent, asymptotically normal, and unbiased for discrete variables. It converges at minimax-optimal rates, which are established as a by-product of our analysis. To understand the effect of adding noise, we further study its asymptotic efficiency and finite sample bias in the univariate discrete case. Simulations show that the estimator is competitive on finite samples. The analysis suggests that similar properties can be expected for other jittering estimators.