Inference robust to outliers with L1‐norm penalization

Jad Beyhum
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Jad Beyhum: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: 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.

Keywords: Robust regression; L1-norm penalization; Unknown variance (search for similar items in EconPapers)
Date: 2020-11
Note: View the original document on HAL open archive server: https://hal.science/hal-03235868v1
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Published in ESAIM: Probability and Statistics, 2020, 24, pp.688-702. ⟨10.1051/ps/2020014⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03235868

DOI: 10.1051/ps/2020014

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