Valid Confidence Intervals for μ,σ When There Is Only One Observation Available

被引：0

作者：

Dasgupta, Anirban ^{[1
]}

Portnoy, Stephen ^{[2
,3
]}

机构：

[1] Purdue Univ, Dept Stat, W Lafayette, IN 47907 USA

[2] Univ Illinois, Dept Stat, Champaign, IL USA

[3] Portland State Univ, Dept Math & Stat, Portland, OR USA

来源：

SANKHYA-SERIES A-MATHEMATICAL STATISTICS AND PROBABILITY | 2024年

关键词：

Confidence interval/s; One sample value; Multivariate normal; Symmetric unimodal; Coverage probability; Non-central chi-square; Compact support;

D O I：

10.1007/s13171-023-00338-2

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：

Portnoy (The American Statistician, 73:1, 10-15, 2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation X similar to N (mu, sigma(2)). Here we extend this result to obtaining 1-sample confidence intervals for sigma and to cases of symmetric unimodal distributions and of distributions with compact support. Finally, we extend the multivariate result in Portnoy (The American Statistician, 73:1, 10-15, 2019) to allow a sample of size m from a multivariate normal distribution where m may be less than the dimension.

引用

页数：12

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