改进James-Stein估计量：通过其正部的有限和截断
Improving the James-Stein estimator via finite-sum truncation of its positive-part
AI总结：
针对高维正态均值估计，通过有限和截断正部函数构造光滑收缩估计量，在满足截断次数条件下优于James-Stein估计量。
AI中文摘要：
在二次损失下估计$p$维正态分布（$p \ge 3$）的均值向量时，正部James-Stein估计量支配原始James-Stein估计量，但它具有非光滑的阈值边界。本文通过将正部函数的无穷级数表示截断为次数为$m$的有限和，提出了一类新的光滑收缩估计量。我们证明了所提出的估计量在任意维度$p \ge 3$下支配James-Stein估计量，只要截断次数满足$m \ge 0.95\sqrt{p-2}$。
英文摘要：
For estimating the mean vector of a $p$-variate normal distribution ($p \ge 3$) under quadratic loss, the positive-part James--Stein estimator dominates the original James--Stein estimator, but it possesses a non-smooth thresholding boundary. In this paper, by truncating the infinite series representation of the positive-part function to a finite sum of degree $m$, we propose a new class of smooth shrinkage estimators. We prove that the proposed estimator dominates the James--Stein estimator for any dimension $p \ge 3$, provided the truncation degree satisfies $m \ge 0.95\sqrt{p-2}$.
