DETECTING RARE AND FAINT SIGNALS VIA THRESHOLDING MAXIMUM LIKELIHOOD ESTIMATORS

• 成果类型: Article
• 署名作者: Qiu, Yumou; Chen, Song Xi; Nettleton, Dan
• 署名单位: University of Nebraska System; University of Nebraska Lincoln; Peking University; Peking University; Iowa State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1574
• 发表日期: 2018
• 页码: 895-923
• 关键词: high-dimensional data; HIGHER CRITICISM; tests

摘要

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 Cramer-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.