an:07285909
Zbl 1455.62065
Beyhum, Jad
Inference robust to outliers with \(\ell_1\)-norm penalization
EN
ESAIM, Probab. Stat. 24, 688-702 (2020).
1292-8100 1262-3318
2020
j
62F35 62J05 62J07 60F10
robust regression; \(\ell_1\)-norm penalization; unknown variance; outliers
Summary: 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 \(\ell_1\)-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.