Estimation with Incompletely Specified Loss Functions (the Case of Several Location Parameters)

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Abstract
If p ≥ 3 separate normal means are to be estimated, the usual, invariant estimator is “inadmissible” if the p separate loss functions can be pooled into a single loss function for the ensemble-of-means problem. Here, we formulate a version of the problem where the losses cannot be pooled in this way, and find a surprisingly weak necessary and sufficient condition under which the usual estimator is inadmissible in a sense appropriate to this formulation. We also examine the spherically symmetric case and find a different necessary and sufficient condition there.

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