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.

翻译：我们考虑在二次损失函数下，对服从$X\sim N_p(\theta,I)$的$p$维正态均值进行估计。研究了去偏收缩估计量的决策理论性质，该估计量对于较小的$\|x\|^2$向原点收缩，而对于较大的$\|x\|^2$则恰好等于无偏估计量$X$。这种去偏收缩估计量看似优于无偏估计量$X$，这意味着极小极大性。然而，我们证明在温和条件下它并非极小极大。