CIRJE-F-749 "Non-minimaxity of Linear Combinations of Restricted Location Estimators and Related Problems"
Author Name Kubokawa, Tatsuya and William E. Strawderman
Date July 2010
Full Paper PDF file
Remarks @@Forthcoming in Journal of the Japan Statistical Society.
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.