Journal Article

On a Generalized False Discovery Rate

Sarkar, Sanat K., Guo, Wenge

2009

Overview

The concept of k-FWER has received much attention lately as an appropriate error rate for multiple testing when one seeks to control at least k false rejections, for some fixed k ≥ 1. A less conservative notion, the k-FDR, has been introduced very recently by Sarkar [Ann. Statist. 34 (2006) 394-415], generalizing the false discovery rate of Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289-300]. In this article, we bring newer insight to the k-FDR considering a mixture model involving independent p-values before motivating the developments of some new procedures that control it. We prove the k-FDR control of the proposed methods under a slightly weaker condition than in the mixture model. We provide numerical evidence of the proposed methods' superior power performance over some k-FWER and k-FDR methods. Finally, we apply our methods to a real data set.

• Publisher: Institute of Mathematical Statistics,The Institute of Mathematical Statistics
• Subject: 62H99 / 62J15 / Average power / Critical values / Data sampling / Error rates / Errors / Exact sciences and technology / gene expression / General topics / generalized FDR / generalized FWER / Logical givens / Mathematical procedures / Mathematics / multiple hypothesis testing / Null hypothesis / oracle k-FDR procedure / Oracles / P values / Point estimators / Probability / Probability and statistics / Random variables / Sciences and techniques of general use / Statistics / stepup procedures / Studies