2021/12/16 by Rida Benhaddou, Benhaddou, Rida, Matthew Connell +1
Computer Science · Mathematics · #62G05 #62G08 #62G20 #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2112.09050
openalex publication_date 2021/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we delve into the nonparametric empirical Bayes theory and approximate the classical Bayes estimator by a truncation of the generalized Laguerre series and then estimate its coefficients by minimizing the prior risk of the estimator. The minimization process yields a system of linear equations the size of which is equal to the truncation level. We focus on the empirical Bayes estimation problem when the mixing distribution, and therefore the prior distribution, has a support on the positive real half-line or a subinterval of it. By investigating several common mixing distributions, we develop a strategy on how to select the parameter of the generalized Laguerre function basis so that our estimator possesses a finite variance. We show that our generalized Laguerre empirical Bayes approach is asymptotically optimal in the minimax sense. Finally, our convergence rate is compared and contrasted with several results from the literature.