Abstract
Abstract This article illuminates some aspects of unbiased estimation. It addresses optimal combination of two dependent unbiased estimators whose variances and correlations are known. When applied to the problem of estimating a location parameter for the uniform distribution, it was found that the optimal mix between mean and median is (3/2)(mean) — (1/2)(median). In cases in which uniformly minimum variance unbiased (UMVU) estimators exist, the approach can be used to give simple expressions for the correlation between the UMVU estimator and any other unbiased estimator. This correlation is always positive. The theory and examples given are well suited for classroom use at the senior undergraduate or beginning graduate level.
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