Detecting rare and faint signals via thresholding maximum likelihood estimators
Yumou Qiu, Song Xi Chen, Dan Nettleton
The Annals of Statistics · 2018 · Volume 46 · Issue 2
Abstract
Motivated by the analysis of RNA sequencing (RNA-seq) data for genes differentially expressed across multiple conditions, we consider detecting rare and faint signals in high-dimensional response variables. We address the signal detection problem under a general framework, which includes generalized linear models for count-valued responses as special cases. We propose a test statistic that carries out a multi-level thresholding on maximum likelihood estimators (MLEs) of the signals, based on a new Cramér-type moderate deviation result for multidimensional MLEs. Based on the multi-level thresholding test, a multiple testing procedure is proposed for signal identification. Numerical simulations and a case study on maize RNA-seq data are conducted to demonstrate the effectiveness of the proposed approaches on signal detection and identification.
Keywords
62G20, 62G32, 62H15, Detection boundary, false discovery proportion, generalized linear model, Moderate deviation, multiple testing procedure, RNA-seq data
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