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Non-minimaxity of Linear Combinations of Restricted Location Estimators and Related Problems
Kubokawa, Tatsuya
98609
Strawderman, William E.
98610
335
Decision theory
linear combination
location parameter
maximum likelihood estimator
restricted parameter
restricted estimator
scale parameter
truncated estimator
application/pdf
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.
Forthcoming in Journal of the Japan Statistical Society.
本文フィルはリンク先を参照のこと
technical report
日本経済国際共同センター
2010-07
Discussion paper series. CIRJE-F
CIRJE-F-749
AA11450569
eng
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2010/2010cf749ab.html
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