Detecting Rare and Faint Signals via Thresholding Maximum Likelihood Estimators
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 response variables.
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 Cram\'{e}r type moderate deviation result for multi-dimensional 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.
