Robust group inference for ultrahigh-dimensional linear regression models

Haochen Rao, Xinyue Chen, Weichao Yang and Xu Guo ()
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Haochen Rao: Beijing Normal University
Xinyue Chen: Beijing Normal University
Weichao Yang: Beijing Normal University
Xu Guo: Beijing Normal University

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 6, No 22, 1279-1310

Abstract: Abstract In this paper, we consider robust group inference for ultrahigh-dimensional linear regression models. For high-dimensional data, outliers or heavy-tailed errors often exist. By taking these critical issues into account, we construct a quadratic form statistic based on the Huber loss. Our procedure allows the dimension of both interested covariates and nuisance covariates to be high-dimensional. Theoretically, we establish the asymptotic normality of our proposed test statistic under the null and alternative hypotheses, allowing the presence of outliers or heavy-tailed errors. Simulation results show the robustness of our proposed test in finite-sample settings. The proposed test is also applied to the analysis of riboflavin data.

Keywords: Group testing; Robust inference; Huber loss (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-025-01005-2

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