Model-Free Statistical Inference on High-Dimensional Data

• 成果类型: Article
• 署名作者: Guo, Xu; Li, Runze; Zhang, Zhe; Zou, Changliang
• 署名单位: Beijing Normal University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Nankai University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2310314
• 发表日期: 2025
• 页码: 186-197
• 关键词: false discovery rate; confidence-intervals; variable selection; reduction; regression; tests; variance; regions; parameters

摘要

This article aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we propose a new test statistic and show that its asymptotic distribution is chi(2) distribution whose degree of freedom does not depend on the unknown population distribution. We further conduct power analysis under local alternative hypotheses. In addition, we study how to control the false discovery rate of the proposed chi(2) tests, which are correlated, to identify important predictors under a model-free framework. To this end, we propose a multiple testing procedure and establish its theoretical guarantees. Monte Carlo simulation studies are conducted to assess the performance of the proposed tests and an empirical analysis of a real-world dataset is used to illustrate the proposed methodology. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work.