Optimal Combinations of Pairs of Estimators
by Alan T. Arnholt and Jaimie L. Hebert
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.
Weighted estimator, coefficient of variation, mean squared error
Alan T. Arnholt,
Jaimie L. Hebert,
N. Rao Chaganty
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