Estimating the Common Mean of Several Normal Populations
Thomas E. Norwood Jr, Klaus Hinkelmann
The Annals of Statistics · 1977 · Volume 5 · Issue 5
Abstract
For $x_i \sim N(\mu, \sigma_i^2) (i = 1, 2,\cdots, n)$ and the $x_i
#39;s independent, this paper gives necessary and sufficient conditions under which the weighted average of the $x_i#39;s, with weights proportional to inverses of the sample variances, has uniformly smaller variance than any of the $x_i#39;s.Keywords
62F10, Common mean, different unknown variances, estimation, normal populations, weighted average of sample means
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