Capturing the severity of type II errors in high-dimensional multiple testing

Li He, Sanat K. Sarkar and Zhigen Zhao

Journal of Multivariate Analysis, 2015, vol. 142, issue C, 106-116

Abstract: The severity of type II errors is frequently ignored when deriving a multiple testing procedure, even though utilizing it properly can greatly help in making correct decisions. This paper puts forward a theory behind developing a multiple testing procedure that can incorporate the type II error severity and is optimal in the sense of minimizing a measure of false non-discoveries among all procedures controlling a measure of false discoveries. The theory is developed under a general model allowing arbitrary dependence by taking a compound decision theoretic approach to multiple testing with a loss function incorporating the type II error severity. We present this optimal procedure in its oracle form and offer numerical evidence of its superior performance over relevant competitors.

Keywords: Bayes rule; Compound decision theory; Oracle procedure; Multiple testing; Weighted marginal false discovery rate; Weighted marginal false non-discovery rate (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2015.08.005

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