Beyhum, Jad (2020) Inference robust to outliers with L1‐norm penalization. ESAIM: Probability and Statistics, vol.24. pp. 688-702.

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Identification Number : 10.1051/ps/2020014


This paper considers the problem of inference in a linear regression model with outliers where the number of outliers can grow with sample size but their proportion goes to 0.
We apply an estimator penalizing the `1-norm of a random vector which is non-zero for
outliers. We derive rates of convergence and asymptotic normality. Our estimator has the same asymptotic variance as the OLS estimator in the standard linear model. This enables to build tests and confidence sets in the usual and simple manner. The proposed procedure is also computationally advantageous as it amounts to solving a convex optimization program. Overall, the suggested approach constitutes a practical robust alternative to the ordinary least squares estimator.

Item Type: Article
Language: English
Date: November 2020
Refereed: Yes
Place of Publication: Les Ulis, France
Uncontrolled Keywords: robust regression, L1-norm penalization, unknown variance.
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 26 May 2021 07:20
Last Modified: 26 May 2021 07:20
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