Statistical Inference for High-Dimensional Generalized Linear Models With Binary Outcomes

• 成果类型: Article
• 署名作者: Cai, T. Tony; Guo, Zijian; Ma, Rong
• 署名单位: University of Pennsylvania; Rutgers University System; Rutgers University New Brunswick; Stanford University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1990769
• 发表日期: 2023
• 页码: 1319-1332
• 关键词: confidence-intervals; regression; selection; regions; tests

摘要

This article develops a unified statistical inference framework for high-dimensional binary generalized linear models (GLMs) with general link functions. Both unknown and known design distribution settings are considered. A two-step weighted bias-correction method is proposed for constructing confidence intervals (CIs) and simultaneous hypothesis tests for individual components of the regression vector. Minimax lower bound for the expected length is established and the proposed CIs are shown to be rate-optimal up to a logarithmic factor. The numerical performance of the proposed procedure is demonstrated through simulation studies and an analysis of a single cell RNA-seq dataset, which yields interesting biological insights that integrate well into the current literature on the cellular immune response mechanisms as characterized by single-cell transcriptomics. The theoretical analysis provides important insights on the adaptivity of optimal CIs with respect to the sparsity of the regression vector. New lower bound techniques are introduced and they can be of independent interest to solve other inference problems in high-dimensional binary GLMs.