Abstract
Abstract A generalization of the Pitman nearness criterion for comparing estimators when the criterion for accuracy is based on a loss function is developed. The concept is applicable to multi-parameter problems. The generalized criterion is then used with invariance to find best estimators of a location or scale parameter. These best estimators do not depend on the form of the loss function provided that it satisfies some reasonable conditions. Thus, the generalized criterion is useful for finding a best estimator when the exact loss function is not known. Some examples are given which establish an additional optimality property of some commonly used estimators.
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