MVUE for the mean with one observation: Normal with same mean and variance

被引：5

作者：

Mukhopadhyay, N ^{[1
]}

机构：

[1] Univ Connecticut, Dept Stat, Storrs, CT 06269 USA

来源：

AMERICAN STATISTICIAN | 2006年 / 60卷 / 01期

关键词：

maximum likelihood estimator; minimum variance; Rao-Blackwellization; unbiased estimation;

D O I：

10.1198/000313006X90774

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Based on one observation X from a N(theta, theta) distribution where theta(> 0) is an unknown parameter, this article provides an exact expression of the minimum variance unbiased estimator of 0 based on the complete and sufficient statistic vertical bar X vertical bar. Even though N(theta, theta) belongs to a one-parameter exponential family, I discuss some small surprises and intricacies that are worth noting.

引用

页码：71 / 74

页数：4

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