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November, 1974 On Estimating the Common Mean of Two Normal Distributions
Arthur Cohen, Harold B. Sackrowitz
Ann. Statist. 2(6): 1274-1282 (November, 1974). DOI: 10.1214/aos/1176342878

Abstract

Consider the problem of estimating the common mean of two normal distributions. Two new unbiased estimators of the common mean are offered for the equal sample size case. Both are better than the sample mean based on one population for sample sizes of 5 or more. A slight modification of one of the estimators is better than either sample mean simultaneously for sample sizes of 10 or more. This same estimator has desirable large sample properties and an explicit simple upper bound is given for its variance. A final result is concerned with confidence estimation. Suppose the variance of the first population, say, is known. Then if the sample mean of that population, plus and minus a constant, is used as a confidence interval, it is shown that an improved confidence interval can be found provided the sample sizes are at least 3.

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Arthur Cohen. Harold B. Sackrowitz. "On Estimating the Common Mean of Two Normal Distributions." Ann. Statist. 2 (6) 1274 - 1282, November, 1974. https://doi.org/10.1214/aos/1176342878

Information

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

zbMATH: 0294.62037
MathSciNet: MR365851
Digital Object Identifier: 10.1214/aos/1176342878

Subjects:
Primary: 62F10
Secondary: 62C15

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 6 • November, 1974
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