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September, 1977 Estimating the Common Mean of Several Normal Populations
Thomas E. Norwood Jr, Klaus Hinkelmann
Ann. Statist. 5(5): 1047-1050 (September, 1977). DOI: 10.1214/aos/1176343959

Abstract

For $x_i \sim N(\mu, \sigma_i^2) (i = 1, 2,\cdots, n)$ and the $x_i$'s independent, this paper gives necessary and sufficient conditions under which the weighted average of the $x_i$'s, with weights proportional to inverses of the sample variances, has uniformly smaller variance than any of the $x_i$'s.

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Thomas E. Norwood Jr. Klaus Hinkelmann. "Estimating the Common Mean of Several Normal Populations." Ann. Statist. 5 (5) 1047 - 1050, September, 1977. https://doi.org/10.1214/aos/1176343959

Information

Published: September, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0368.62018
MathSciNet: MR448679
Digital Object Identifier: 10.1214/aos/1176343959

Subjects:
Primary: 62F10

Keywords: Common mean , different unknown variances , estimation , normal populations , weighted average of sample means

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 5 • September, 1977
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