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C. R. Rao (1981) has noted that shrinking the mean squared error of an unbiased estimator to a minimum mean squared error estimator does not necessarily yield an estimator which is better in the sense of Pitman Nearness. For an absolute error loss function, Rao's observations are shown to be uniformly true for certain estimation problems.
Sankhyā: The Indian Journal of Statistics, Series B (1960-2002) © 1985 Indian Statistical Institute