preprint · arXiv (Cornell University) · 2024
Matrix norm shrinkage estimators and priors
Xiao Li, Takeru Matsuda, Fumiyasu Komaki
Cited by 0Open access
Abstract
We develop a class of minimax estimators for a normal mean matrix under the Frobenius loss, which generalizes the James--Stein and Efron--Morris estimators. It shrinks the Schatten norm towards zero and works well for low-rank matrices. We also propose a class of superharmonic priors based on the Schatten norm, which generalizes Stein's prior and the singular value shrinkage prior. The generalized Bayes estimators and Bayesian predictive densities with respect to these priors are minimax. We examine the performance of the proposed estimators and priors in simulation.
Cite this paper
Li, X., Matsuda, T., & Komaki, F. (2024). Matrix norm shrinkage estimators and priors. arXiv (Cornell University). https://doi.org/10.48550/arxiv.2406.06137
Li, Xiao, et al. “Matrix norm shrinkage estimators and priors.” arXiv (Cornell University), 2024, https://doi.org/10.48550/arxiv.2406.06137.
Li, Xiao, Takeru Matsuda, and Fumiyasu Komaki. 2024. “Matrix norm shrinkage estimators and priors.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.2406.06137.
Li, X., Matsuda, T. and Komaki, F. (2024) ‘Matrix norm shrinkage estimators and priors’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.2406.06137.
@misc{li2024matrix,
title = {{Matrix norm shrinkage estimators and priors}},
author = {Li, Xiao and Matsuda, Takeru and Komaki, Fumiyasu},
journal = {arXiv (Cornell University)},
year = {2024},
doi = {10.48550/arxiv.2406.06137}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.