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Non-minimaxity of debiased shrinkage estimators (2306.04232v1)
Published 7 Jun 2023 in math.ST and stat.TH
Abstract: We consider the estimation of the $p$-variate normal mean of $X\sim N_p(\theta,I)$ under the quadratic loss function. We investigate the decision theoretic properties of debiased shrinkage estimator, the estimator which shrinks towards the origin for smaller $|x|2$ 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.