PreprintarXiv licencearXiv
Improving the James-Stein estimator via q-number shrinkage
Abstract
For estimating the mean vector of a p-variate normal distribution (p ≥ 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 ≥ 3, provided the truncation parameter satisfies m ≥ 0.95√(p−2).
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BibTeX
@misc{maruyama2026improving,
title = {{Improving the James-Stein estimator via q-number shrinkage}},
author = {Yuzo Maruyama and Akimichi Takemura},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39614},
eprint = {2609.39614},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39614},
}
RIS
TY - UNPB
TI - Improving the James-Stein estimator via q-number shrinkage
AU - Yuzo Maruyama
AU - Akimichi Takemura
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2609.39614
UR - https://arxiv.org/abs/2609.39614
AB - For estimating the mean vector of a p-variate normal distribution (p ≥ 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 ≥ 3, provided the truncation parameter satisfies m ≥ 0.95√(p−2).
ER -