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Inference robust to outliers with L1‐norm penalization

Beyhum, Jad (2019) Inference robust to outliers with L1‐norm penalization. TSE Working Paper, n. 19-1032, Toulouse

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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: Monograph (Working Paper)
Language: English
Date: August 2019
Place of Publication: Toulouse
Uncontrolled Keywords: robust regression, L1-norm penalization, unknown variance.
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 29 Aug 2019 13:48
Last Modified: 29 Aug 2019 13:48
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