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Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models

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  • Rong Ma
  • T. Tony Cai
  • Hongzhe Li

Abstract

High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this article, 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 and falsely discovered variables 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 dataset of a metabolomics study that investigates the association between fecal metabolites and pediatric Crohn’s disease and the effects of treatment on such associations. Supplementary materials for this article are available online.

Suggested Citation

  • Rong Ma & T. Tony Cai & Hongzhe Li, 2021. "Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 984-998, April.
    • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:534:p:984-998
    DOI: 10.1080/01621459.2019.1699421
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    Cited by:

    1. Shengfei Tang & Yanmei Shi & Qi Zhang, 2023. "Bias-Corrected Inference of High-Dimensional Generalized Linear Models," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    2. Mingrui Zhong & Zanhua Yin & Zhichao Wang, 2023. "Variable Selection for Sparse Logistic Regression with Grouped Variables," Mathematics, MDPI, vol. 11(24), pages 1-21, December.
    3. Panxu Yuan & Yinfei Kong & Gaorong Li, 2024. "FDR control and power analysis for high-dimensional logistic regression via StabKoff," Statistical Papers, Springer, vol. 65(5), pages 2719-2749, July.
    4. Xiaorui Zhu & Yichen Qin & Peng Wang, 2023. "Sparsified Simultaneous Confidence Intervals for High-Dimensional Linear Models," Papers 2307.07574, arXiv.org.
    5. Lu Xia & Bin Nan & Yi Li, 2023. "Debiased lasso for generalized linear models with a diverging number of covariates," Biometrics, The International Biometric Society, vol. 79(1), pages 344-357, March.

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