Optimal Combinations of Pairs of Estimators

by Alan T. Arnholt and Jaimie L. Hebert .

Abstract: Several authors consider the optimization of linear combinations of independent estimators with respect to mean squared error. The minimization of variance for convex combinations of estimators having a known correlation coefficient is also considered in the literature. We unify and generalize the results pertaining to these two problems by minimizing mean squared error for linear combinations of dependent estimators. We examine the role of the correlation coefficient in establishing the optimal weights for these combinations and uncover a relationship between these optimal weights and those provided in the literature for minimizing the mean squared error of a single estimator.

Key Words: Weighted estimator, coefficient of variation, mean squared error

Authors:
Alan T. Arnholt, arnholt@math.appstate.edu
Jaimie L. Hebert, mth_jlh@shsu.edu

Editor: N. Rao Chaganty , rchagant@odu.edu

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