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What is Learnable in Valiant's Theory of the Learnable? 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Non-minimaxity of debiased shrinkage estimators
Yuzo Maruyama, Akimichi Takemura · 2023-06-07 · via math.ST updates on arXiv.org

We consider the estimation of the $p$-variate normal mean of $X\sim N_p(θ,I)$ 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.

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