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September, 1974 Point and Confidence Estimation of a Common Mean and Recovery of Interblock Information
L. D. Brown, Arthur Cohen
Ann. Statist. 2(5): 963-976 (September, 1974). DOI: 10.1214/aos/1176342817

Abstract

Consider the problem of estimating a common mean of two independent normal distributions, each with unknown variances. Note that the problem of recovery of interblock information in balanced incomplete blocks designs is such a problem. Suppose a random sample of size $m$ is drawn from the first population and a random sample of size $n$ is drawn from the second population. We first show that the sample mean of the first population can be improved on (with an unbiased estimator having smaller variance), provided $m \geqq 2$ and $n \geqq 3$. The method of proof is applicable to the recovery of information problem. For that problem, it is shown that interblock information could be used provided $b \geqq 4$. Furthermore for the case $b = t = 3$, or in the common mean problem, where $n = 2$, it is shown that the prescribed estimator does not offer improvement. Some of the results for the common mean problem are extended to the case of $K$ means. Results similar to some of those obtained for point estimation, are also obtained for confidence estimation.

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L. D. Brown. Arthur Cohen. "Point and Confidence Estimation of a Common Mean and Recovery of Interblock Information." Ann. Statist. 2 (5) 963 - 976, September, 1974. https://doi.org/10.1214/aos/1176342817

Information

Published: September, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0305.62019
MathSciNet: MR356334
Digital Object Identifier: 10.1214/aos/1176342817

Subjects:
Primary: 62F10
Secondary: 62C15 , 62K10

Keywords: balanced incomplete blocks designs , Common mean , confidence intervals , inadmissibility , interblock information , unbiased estimators

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 5 • September, 1974
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