Robust Weighted Lad Regression

22 Pages Posted: 3 Nov 2008

See all articles by Avi Giloni

Avi Giloni

Independent

Jeffrey S. Simonoff

New York University (NYU) - Leonard N. Stern School of Business; New York University (NYU) - Department of Information, Operations, and Management Sciences

Bhaskar Sengupta

affiliation not provided to SSRN

Date Written: February 2005

Abstract

The least squares linear regression estimator is well-known to be highly sensitive tounusual observations in the data, and as a result many more robust estimators havebeen proposed as alternatives. One of the earliest proposals was least-sum of absolutedeviations (LAD) regression, where the regression coefficients are estimated throughminimization of the sum of the absolute values of the residuals. LAD regression hasbeen largely ignored as a robust alternative to least squares, since it can be stronglyaffected by a single observation (that is, it has a breakdown point of 1/n, where n isthe sample size). In this paper we show that judicious choice of weights can resultin a weighted LAD estimator with much higher breakdown point. We discuss the properties of the weighted LAD estimator, and show via simulation that its performance is competitive with that of high breakdown regression estimators, particularly in thepresence of outliers located at leverage points. We also apply the estimator to several real data sets.

Keywords: Breakdown point, Leverage points, Outliers, Robust regression

Suggested Citation

Giloni, Avi and Simonoff, Jeffrey S. and Sengupta, Bhaskar, Robust Weighted Lad Regression (February 2005). Statistics Working Papers Series, Vol. , pp. -, 2005. Available at SSRN: https://ssrn.com/abstract=1293597

Avi Giloni (Contact Author)

Independent

No Address Available

Jeffrey S. Simonoff

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

New York University (NYU) - Department of Information, Operations, and Management Sciences

44 West Fourth Street
New York, NY 10012
United States

Bhaskar Sengupta

affiliation not provided to SSRN

No Address Available

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