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A stochastic process approach to false discovery control. (English) Zbl 1092.62065
Summary: This paper extends the theory of false discovery rates (FDR) pioneered by Y. Benjamini and Y. Hochberg [J. R. Stat. Soc., Ser. B 57, No. 1, 289–300 (1995; Zbl 0809.62014)]. We develop a framework in which the False Discovery Proportion (FDP) – the number of false rejections divided by the number of rejections – is treated as a stochastic process. After obtaining the limiting distribution of the process, we demonstrate the validity of a class of procedures for controlling the False Discovery Rate (the expected FDP). We construct a confidence envelope for the whole FDP process. From these envelopes we derive confidence thresholds, for controlling the quantiles of the distribution of the FDP as well as controlling the number of false discoveries. We also investigate methods for estimating the \(p\)-value distribution.

62H15 Hypothesis testing in multivariate analysis
62M99 Inference from stochastic processes
62E20 Asymptotic distribution theory in statistics
62G10 Nonparametric hypothesis testing
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