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Poster
Robust Inference for High-Dimensional Linear Models via Residual Randomization
Y. Samuel Wang · Si Kai Lee · Panos Toulis · Mladen Kolar

Wed Jul 21 09:00 AM -- 11:00 AM (PDT) @
in Poster Session 3 »

We propose a residual randomization procedure designed for robust inference using Lasso estimates 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.

Keywords: Statistical Learning Theory

Author Information

Y. Samuel Wang (University of Chicago)
Si Kai Lee (Chicago Booth School of Business)
Panos Toulis (Chicago Booth School of Business)
Mladen Kolar (University of Chicago Booth School of Business)

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