One-Step R-Estimation in Linear Models with Stable Errors

13 Pages Posted: 22 Oct 2010

See all articles by Marc Hallin

Marc Hallin

ECARES, Universite Libre de Bruxelles

Yvik Swan

Université Libre de Bruxelles (ULB) - Department of Mathematics

Thomas Verdebout

University of Lille III - EQUIPPE-GREMARS

David Veredas

Vlerick Business School

Date Written: October 21, 2010

Abstract

Classical estimation techniques for linear models either are inconsistent, or perform somewhat poorly under stable error densities; most of them are not even rate-optimal. In this paper, we develop an original R-estimation method and investigate its asymptotic performances under stable densities. Contrary to traditional least squares, the proposed R-estimators, remain root-n consistent (the optimal rate) under the whole family of stable distributions, irrespective of their asymmetry and tail index. While stable-likelihood estimation, due to the absence of a closed form for stable densities, is generally considered unfeasible, our method allows us to construct estimators reaching the parametric efficiency bounds associated with any prescribed values of tail index alpha and the skewness parameter beta, while preserving root-n consistency under any alpha and beta. The method furthermore avoids all forms of multidimensional argmin computation. Simulations confirm its excellent finite-sample performances.

Keywords: Stable Distributions, Local Asymptotic Normality, R-Estimation, Asymptotic Relative Efficiencies

Suggested Citation

Hallin, Marc and Swan, Yvik and Verdebout, Thomas and Veredas, David, One-Step R-Estimation in Linear Models with Stable Errors (October 21, 2010). Available at SSRN: https://ssrn.com/abstract=1695537 or http://dx.doi.org/10.2139/ssrn.1695537

Marc Hallin

ECARES, Universite Libre de Bruxelles ( email )

Ave. Franklin D Roosevelt, 50 - C.P. 114
Brussels, B-1050
Belgium
+32 2 650 5886 (Phone)
+32 2 650 5899 (Fax)

Yvik Swan

Université Libre de Bruxelles (ULB) - Department of Mathematics ( email )

Brussels
Belgium

Thomas Verdebout

University of Lille III - EQUIPPE-GREMARS ( email )

Lille
France

David Veredas (Contact Author)

Vlerick Business School ( email )

Library
REEP 1
Gent, BE-9000
Belgium