Non-minimaxity of debiased shrinkage estimators

06/07/2023

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by   Yuzo Maruyama, et al.

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We consider the estimation of the p-variate normal mean of X∼ N_p(θ,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 x^2 and which is exactly equal to the unbiased estimator X for larger x^2. Such debiased shrinkage estimator seems superior to the unbiased estimator X, which implies minimaxity. However we show that it is not minimax under mild conditions.