2016/04/26 by Ery Arias-Castro, Arias-Castro, Ery, Shiyun Chen +1 · 4 citations
Mathematics · #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1604.07520
openalex publication_date 2016/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a stylized multiple testing problem where the test statistics are independent and assumed to have the same distribution under their respective null hypotheses. We first show that, in the normal means model where the test statistics are normal Z-scores, the well-known method of (Benjamini and Hochberg, 1995) is optimal in some asymptotic sense. We then show that this is also the case of a recent distribution-free method proposed by Foygel-Barber and Candès (2015). The method is distribution-free in the sense that it is agnostic to the null distribution - it only requires that the null distribution be symmetric. We extend these optimality results to other location models with a base distribution having fast-decaying tails.