Non-minimaxity of Linear Combinations of Restricted Location Estimators and Related Problems

Tatsuya Kubokawa and William E. Strawderman
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Tatsuya Kubokawa: Faculty of Economics, University of Tokyo
William E. Strawderman: Department of Statistics, Rutgers University

No CIRJE-F-749, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: The estimation of a linear combination of several restricted location parameters is addressed from a decision-theoretic point of view. The corresponding linear combination of the best location equivariant and the unrestricted unbiased estimators is minimax. Since the locations are restricted, it is reasonable to use the linear combination of the restricted estimators such as maximum likelihood estimators. In this paper, a necessary and sufficient condition for such restricted estimators to be minimax is derived, and it is shown that the restricted estimators are not minimax when the number of the location parameters is large. The condition for the minimaxity is examined for some specific distributions. Finally, similar problems of estimating the product and sum of the restricted scale parameters are studied, and it is shown that similar non-dominance properties appear when the number of the scale parameters is large.

Pages: 23pages
Date: 2010-07
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