On a generalized false discovery rate. (English) Zbl 1161.62041

Summary: 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 \(k\geq 1\). A less conservative notion, the \(k\)-FDR, has been introduced very recently by S. K. Sarkar [ibid. 34, No. 1, 394–415 (2006; Zbl 1091.62060)], generalizing the false discovery rate of Y. Benjamini and Y. Hochberg [J. R. Stat. Soc., Ser. B 57, No. 1, 289–300 (1995; Zbl 0809.62014)]. 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.


62J15 Paired and multiple comparisons; multiple testing
62H99 Multivariate analysis
65C60 Computational problems in statistics (MSC2010)
Full Text: DOI arXiv


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