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Non-minimaxity of debiased shrinkage estimators

Abstract

We consider the estimation of the pp-variate normal mean of XNp(θ,I)X\sim N_p(\theta,I) under the quadratic loss function. We investigate the decision theoretic properties of debiased shrinkage estimator, the estimator which shrinks towards the origin for smaller x2\|x\|^2 and which is exactly equal to the unbiased estimator XX for larger x2\|x\|^2. Such debiased shrinkage estimator seems superior to the unbiased estimator XX, which implies minimaxity. However we show that it is not minimax under mild conditions.

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