A Scan Procedure for Multiple Testing

2018/08/02 by Chen, Shiyun, Ying, Andrew, Arias-Castro, Ery
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1808.00631

Abstract

In a multiple testing framework, we propose a method that identifies the interval with the highest estimated false discovery rate of P-values and rejects the corresponding null hypotheses. Unlike the Benjamini-Hochberg method, which does the same but over intervals with an endpoint at the origin, the new procedure `scans' all intervals. In parallel with \citep*storey2004strong, we show that this scan procedure provides strong control of asymptotic false discovery rate. In addition, we investigate its asymptotic false non-discovery rate, deriving conditions under which it outperforms the Benjamini-Hochberg procedure. For example, the scan procedure is superior in power-law location models.

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