Tests for high-dimensional generalized linear models under general covariance structure

Weichao Yang, Xu Guo and Lixing Zhu

Computational Statistics & Data Analysis, 2024, vol. 199, issue C

Abstract: This study investigates the testing of regression coefficients within high-dimensional generalized linear models featuring general covariance structures. The derived asymptotic properties reveal that distinct covariance structures can lead to varying limiting null distributions, including the normal distribution, for a widely employed quadratic-norm based test statistic. This circumstance renders it infeasible to determine critical values through a limiting null distribution. In response to this challenge, we propose a multiplier bootstrap test procedure for practical implementation. Additionally, we introduce a modified version of this procedure, incorporating projection when dealing with nuisance parameters. We then proceed to examine the asymptotic level and power of the proposed tests and assess their finite-sample performance through simulations. Finally, we present a real data analysis to illustrate the practical application of the proposed tests.

Keywords: High-dimensional inference; U-statistics; Multiplier bootstrap; Nuisance parameter (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:199:y:2024:i:c:s0167947324001105

DOI: 10.1016/j.csda.2024.108026

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