Minimaxity under the half-Cauchy prior
Statistics Theory
2024-06-14 v1 Statistics Theory
Abstract
This is a follow-up paper of Polson and Scott (2012, Bayesian Analysis), which claimed that the half-Cauchy prior is a sensible default prior for a scale parameter in hierarchical models. For estimation of a p-variate normal mean under the quadratic loss, they demonstrated that the Bayes estimator with respect to the half-Cauchy prior seems to be minimax through numerical experiments. In this paper, we theoretically establish the minimaxity of the corresponding Bayes estimator using the interval arithmetric.
Cite
@article{arxiv.2406.08892,
title = {Minimaxity under the half-Cauchy prior},
author = {Yuzo Maruyama and Takeru Matsuda},
journal= {arXiv preprint arXiv:2406.08892},
year = {2024}
}
Comments
The title of this article is quite similar to that of our previous article on arXiv 2308.09339, in which we discussed some variants of the half-Cauchy prior. In this article, we focus on the half-Cauchy prior itself