Minimaxity under the half-Cauchy prior

2024/06/13 by Yuzo Maruyama, Maruyama, Yuzo, Takeru Matsuda +1 · 1 citation
Mathematics · #62C20 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2406.08892

openalex publication_date 2024/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• GRASP: Grouped Regression with Adaptive Shrinkage Priors

Related

• Minimaxity under half-Cauchy type priors
• On the half-Cauchy prior for a global scale parameter
• On Minimax Optimality of Sparse Bayes Predictive Density Estimates
• Asymptotic Minimaxity, Optimal Posterior Concentration and Asymptotic Bayes Optimality of Horseshoe-type Priors Under Sparsity
• Semiparametric posterior limits