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Beyhum, Jad
(2020)
Inference robust to outliers with L1‐norm penalization.
ESAIM: Probability and Statistics, vol.24.
pp. 688-702.
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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.
| 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. |
| Subjects: | B- ECONOMIE ET FINANCE |
| Divisions: | TSE-R (Toulouse) |
| Site: | UT1 |
| Date Deposited: | 26 May 2021 07:20 |
| Last Modified: | 26 May 2021 07:20 |
| OAI Identifier: | oai:tse-fr.eu:125633 |
| URI: | https://publications.ut-capitole.fr/id/eprint/43574 |
Available Versions of this Item
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Inference robust to outliers with L1‐norm penalization. (deposited 29 Aug 2019 13:48)
- Inference robust to outliers with L1‐norm penalization. (deposited 26 May 2021 07:20) [Currently Displayed]
