Sharp regret-Hellinger bounds for Gaussian empirical Bayes via polynomial approximation
借助多项式逼近建立高斯经验贝叶斯的尖锐遗憾界
A central problem in the theory of empirical Bayes is to control the regret (excess risk) of a learned Bayes rule by the Hellinger distance between the estimated and true marginal densities. In the normal means model, the classical result of Jiang and Zhang (2009) achieves this only after regularizing the Bayes rule and incurs an extraneous cubic logarithmic factor through a delicate recursive argument. This paper introduces a new technique, based on polynomial approximation…