Year: 2026
Type: preprint
Abstract: 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 Jame-Stein estimator though it suffers from a non-smooth thresholding boundary. In this paper, we first express the shrinkage factor of the positive-part estimator using an infinite series. Truncating this series at a finite degree $m$ allows us to interpret the factor as a special case of $q$-numbers. Leveraging these $q$-numbers parameterized by a positive real index $m$, we propose a novel smooth estimator. We prove that the proposed estimator dominates the original James-Stein estimator for any dimension $p \ge 3$, provided the truncation parameter satisfies $m \ge 0.95\sqrt{p-2}$.
Source: arXiv (Cornell University)
Authors: Maruyama, Yuzo, Takemura, Akimichi
Institutions: Chiba University, Shiga University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215117665