2018/05/31 by Rong Ma, T. Tony Cai, Tommaso Cai +1
Mathematics · Medicine · #Algorithm #Biology #Computer science #Data mining #False discovery rate #Liver Disease Diagnosis and Treatment #Logistic regression #Mathematical optimization #Mathematics #Minimax #Multiple comparisons problem #Null (SQL) #Null distribution #Null hypothesis #Projection (relational algebra) #Statistic #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistical hypothesis testing #Statistics #Test statistic #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.1080/01621459.2019.1699421
published as Journal of the American Statistical Association (2019) · Typos corrected
openalex publication_date 2020/01/03 · arxiv created 2020/11/19 · arxiv updated 2020/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 lower bound for the global testing is established, which shows that the proposed test is asymptotically minimax optimal over some sparsity range. 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 data set of a metabolomics study that investigates the association between fecal metabolites and pediatric Crohn's disease and the effects of treatment on such associations.