Non-minimaxity of debiased shrinkage estimators

Abstract
We consider the estimation of the -variate normal mean of under the quadratic loss function. We investigate the decision theoretic properties of debiased shrinkage estimator, the estimator which shrinks towards the origin for smaller and which is exactly equal to the unbiased estimator for larger . Such debiased shrinkage estimator seems superior to the unbiased estimator , which implies minimaxity. However we show that it is not minimax under mild conditions.
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