Volume 24, 2020
|Page(s)||688 - 702|
|Published online||04 November 2020|
Inference robust to outliers with ℓ1-norm penalization*
Toulouse School of Economics, Université Toulouse Capitole, Toulouse, France.
** Corresponding author: firstname.lastname@example.org
Accepted: 2 April 2020
This paper considers inference in a linear regression model with outliers in which the number of outliers can grow with sample size while their proportion goes to 0. We propose a square-root lasso ℓ1-norm penalized estimator. We derive rates of convergence and establish asymptotic normality. Our estimator has the same asymptotic variance as the OLS estimator in the standard linear model. This enables us to build tests and confidence sets in the usual and simple manner. The proposed procedure is also computationally advantageous, it amounts to solving a convex optimization program. Overall, the suggested approach offers a practical robust alternative to the ordinary least squares estimator.
Mathematics Subject Classification: 62F35 / 62J05 / 62J07
Key words: Robust regression / ℓ1-norm penalization / unknown variance
I thank my PhD supervisor Professor Eric Gautier for his availability and valuable help. I am also grateful to Anne Ruiz-Gazen, Jean-Pierre Florens, Thierry Magnac, Nour Meddahi, two anonymous referees and an associate editor of ESAIM: Probability & Statistics for their useful comments. I acknowledge financial support from the ERC POEMH 337665 grant.
© EDP Sciences, SMAI 2020
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