Inference robust to outliers with L1‐norm penalization

Jad Beyhum

No 19-1032, TSE Working Papers from Toulouse School of Economics (TSE)

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: 2019-08
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.tse-fr.eu/sites/default/files/TSE/docu ... 2019/wp_tse_1032.pdf Full Text (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:123325

Access Statistics for this paper

More papers in TSE Working Papers from Toulouse School of Economics (TSE) Contact information at EDIRC.
Bibliographic data for series maintained by ().