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<p>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.</p>

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Robust group inference for ultrahigh-dimensional linear regression models

  • 期刊论文

  • 发表日期：

    2025年7月23日

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  • Haochen Rao,
  • Xinyue Chen,
  • Weichao Yang,
  • Xu Guo

摘要

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.