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New development of statistical estimation of parameters with linear inequalities restriction

线性不等式限制参数统计估计的新进展

基本信息

批准号：
22500263
负责人：
WATANABE Genso
金额：
$ 1.5万
依托单位：
Mejiro University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2010
资助国家：
日本
起止时间：
2010 至 2012
项目状态：
已结题

项目摘要

We first consider the problem of estimating the common mean of two normal distributions with unknown ordered variances. We give a broad class of estimators which includes the estimators proposed by Nair (1982) and Elfessi et al. (1992) and show that the estimators stochastically dominate the estimators which do not take into account the order restriction on variances, including the one given by Graybill and Deal (1959).Then we propose a broad class of individual estimators of two ordered means when unknown variances are ordered. We show that in estimating the mean with larger variance, estimators which do not take into account the order restriction on variances are stochastically dominated by the proposed class of estimators which take into account both order restrictions. However, in terms of estimating the mean with smaller variance, similar improvement is not possible even in terms of mean squared error. We also show a domination result in the simultaneous estimation problem of two ordered means. Further, improving upon the unbiased estimators of the two means is also discussed.We also discuss the above problems under Pitman closeness criterion and confirm the validity of Pitman closeness criterion.

我们首先考虑两个有序方差未知的正态分布的共同均值的估计问题。我们给出了一类广泛的估计量，其中包括Nair(1982)和Elfessi等人提出的估计量。(1992)，并证明了估计量随机支配不考虑方差的阶数限制的估计量，包括GrayBill和Deal(1959)给出的估计量。然后，当未知方差被排序时，我们提出了两个有序均值的一类广泛的个体估计。我们证明了在估计具有较大方差的均值时，不考虑对方差的阶数限制的估计量被所提出的同时考虑了阶数限制的估计量所支配。然而，就估计方差较小的均值而言，即使是在均方误差方面，也不可能有类似的改善。我们还证明了两个有序均值同时估计问题的一个控制性结果。在此基础上，对两种方法的无偏估计进行了改进，并讨论了在Pitman贴近准则下的上述问题，证实了Pitman贴近准则的有效性。

项目成果

期刊论文数量（0）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Estimation of two ordered means with two ordered variances under Pitman’s closeness and numerical analysis.

在 Pitman 接近度和数值分析下估计具有两个有序方差的两个有序均值。

DOI：
发表时间：
2012
期刊：
影响因子：
0
作者：
Chang Yuan-Tsung;Shinozaki Nobuo;江島伸興;Chang Yuan-Tsung;張元宗;江島伸興;Chang Yuan-Tsung;Nobuoki Eshima;Chang Yuan-Tsung
通讯作者：
Chang Yuan-Tsung

Improved estimators for the common mean and ordered means of two normal distributions with ordered variances