Partial Gini Covariance-based Robust Inference for High-dimensional Linear Models with Heavy-tailed Errors

原文摘要

This paper introduces a novel robust high-dimensional inference framework based on partial Gini covariance. We specifically address the practically important problem of quantifying how changes in features affect the conditional mean in high-dimensional linear regression when the random noises are heavy-tailed and possibly asymmetric. Conventional high-dimensional regression inference methods suffer from inaccurate type I errors and reduced power in heavy-tailed contexts. While adaptive Huber regression provides a principled remedy, its effectiveness relies on the careful calibration of robustification parameters that must adapt to sample size, dimensionality, and tail behavior. Our proposed approach leverages the partial Gini covariance to construct a robust statistical inference framework that requires minimal tuning and avoids restrictive moment conditions on error distributions. By circumventing the need for error density estimation, this method enhances both computational feasibility and robustness. Extensive simulations and a real-world data example demonstrate the proposed method’s superior power and robustness over standard high-dimensional inference approaches, such as those based on the debiased Lasso. The asymptotic relative efficiency analysis provides additional theoretical insight on the improved efficiency of the new approach in the heavy-tailed setting. Additionally, the partial Gini covariance extends to the multivariate setting, enabling chi-square testing for a group of coefficients.

摘要来源：Taylor & Francis · 出版社摘要