Robust Inference for High-Dimensional Linear Models via Residual Randomization

06/14/2021
by   Y. Samuel Wang, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

12/07/2018

Variable selection in high-dimensional linear model with possibly asymmetric or heavy-tailed errors

We consider the problem of automatic variable selection in a linear mode...
04/18/2019

Adaptive Huber Regression on Markov-dependent Data

High-dimensional linear regression has been intensively studied in the c...
05/04/2018

Lasso, knockoff and Gaussian covariates: a comparison

Given data y and k covariates x_j one problem in linear regression is to...
08/12/2019

Life After Bootstrap: Residual Randomization Inference in Regression Models

We develop a randomization-based method for inference in regression mode...
08/25/2020

Regularization Methods Based on the L_q-Likelihood for Linear Models with Heavy-Tailed Errors

We propose regularization methods for linear models based on the L_q-lik...
03/20/2019

Behavior of Lasso and Lasso-based inference under limited variability

We study the nonasymptotic behavior of Lasso and Lasso-based inference w...
10/01/2015

Similarity of symbol frequency distributions with heavy tails

Quantifying the similarity between symbolic sequences is a traditional p...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.