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arXiv · 1403.5609

Capturing the Severity of Type II Errors in High-Dimensional Multiple Testing

Li He·Sanat K. Sarkar·Zhigen Zhao
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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.

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Li He, Sanat K. Sarkar, Zhigen Zhao. 2014-03-22. Capturing the Severity of Type II Errors in High-Dimensional Multiple Testing. https://arxiv.org/abs/1403.5609

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