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

Author

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  • Yang, Weichao
  • Guo, Xu
  • Zhu, Lixing

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.

Suggested Citation

  • Yang, Weichao & Guo, Xu & Zhu, Lixing, 2024. "Tests for high-dimensional generalized linear models under general covariance structure," Computational Statistics & Data Analysis, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:csdana:v:199:y:2024:i:c:s0167947324001105
    DOI: 10.1016/j.csda.2024.108026
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