We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in settings that also include heavy-tailed covariates and errors. Moreover, our procedure can be valid under clustered errors, which is important in practice, but has been largely overlooked by earlier work. Through extensive simulations, we illustrate our method's wider range of applicability as suggested by theory. In particular, we show that our method outperforms state-of-art methods in challenging, yet more realistic, settings where the distribution of covariates is heavy-tailed or the sample size is small, while it remains competitive in standard, "well behaved" settings previously studied in the literature.
翻译:我们建议了一种为高维环境中基于激光测算的强力激光测算设计的剩余随机化程序。 与早期侧重于亚高加索误差的工作相比, 拟议的程序旨在在包括重尾共变和误差在内的环境中进行强有力的工作。 此外, 我们的程序可以在分组误差下有效, 这在实践上很重要, 但却在很大程度上被先前的工作忽略了。 我们通过广泛的模拟, 展示了我们的方法的更广泛适用范围, 正如理论所建议 。 特别是, 我们显示, 我们的方法在挑战性、 更现实的环境下, 共变的分布是重尾的, 或样本大小很小, 而在标准、 “ 良好行为” 的设置上仍然具有竞争力, 此前在文献中研究过。