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Activity Number: 345 - High-Dimensional Statistics
Type: Contributed
Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #304965
Title: Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models
Author(s): Rong Ma* and T. Tony Cai and Hongzhe Li
Companies: Univ of Pennsylvania and The Wharton School, University of Pennsylvania and University of Pennsylvania
Keywords: False discovery rate; Global testing; Large-scale multiple testing; Minimax lower bound; Logistic regression

High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this paper, global testing and large-scale multiple testing for the regression coefficients are considered in both single- and two-regression settings. A test statistic for testing the global null hypothesis is constructed using a generalized low-dimensional projection for bias correction and its asymptotic null distribution is derived. A minimax lower bound for the global testing is established, which shows that the proposed test is asymptotically minimax optimal. For testing the individual coefficients simultaneously, multiple testing procedures are proposed and shown to control the false discovery rate (FDR) and falsely discovered variables (FDV) asymptotically. Simulation studies are carried out to examine the numerical performance of the proposed tests and their superiority over existing methods. The testing procedures are also illustrated by analyzing a metabolomics study that investigates the association between fecal metabolites and pediatric Crohn's disease and the effects of treatment on such associations.

Authors who are presenting talks have a * after their name.

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