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.
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