Joint confidence sets for the mean and variance of a normal distribution

被引：30

作者：

Arnold, BC ^{[1
]}

Shavelle, RM ^{[1
]}

机构：

[1] Univ Calif Riverside, Dept Stat, Riverside, CA 92521 USA

来源：

AMERICAN STATISTICIAN | 1998年 / 52卷 / 02期

关键词：

confidence region; likelihood ratio test;

D O I：

10.2307/2685471

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：

The standard example of an exact joint confidence set provided in elementary textbooks involves normal data. In addition textbooks provide a variety of asymptotic approximate joint confidence sets for (mu,sigma(2)) in such a setting. What is lacking, and what is provided in this article, is a comparative study of the size and actual performance of these confidence sets. A mild surprise arises in the comparison. If the sample size is 100 or more, the asymptotic confidence regions, in addition to being more robust to violations of distributional assumptions, actually outperform the exact region in terms of expected area of the regions.

引用

页码：133 / 140

页数：8

共 20 条

[1] AITCHISON J, 1964, J ROY STAT SOC B, V26, P462
[2] AITCHISON J, 1965, J ROY STAT SOC B, V27, P245
[3] [Anonymous], 1979, The Advanced Theory of Statistics
[4] BARTLETT MS, 1955, BIOMETRIKA, V42, P201, DOI 10.1093/biomet/42.1-2.201
[5] BROWNLEE KA, 1963, STAT THEORY METHODOL
[6] CONFIDENCE BANDS FOR CUMULATIVE DISTRIBUTION-FUNCTIONS OF CONTINUOUS RANDOM-VARIABLES
CHENG, RCH
ILES, TC
[J]. TECHNOMETRICS, 1983, 25 (01) : 77 - 86
[7] Cramer H., 1951, MATH METHODS STAT
[8] CONFIDENCE-REGIONS FOR PARAMETER PAIRS
DOUGLAS, JB
[J]. AMERICAN STATISTICIAN, 1993, 47 (01) : 43 - 45
[9] ELDERTON WP, 1920, PRIMER STAT
[10] FIELLER EC, 1954, J ROY STAT SOC B, V16, P175

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