One-step R-estimation in linear models with stable errors

M. Hallin, Y. Swan, T. Verdebout, D. Veredas

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under α-stable error densities; most of them are not even rate-optimal. In this paper, we propose an original one-step 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 parametric stable-likelihood estimation, due to the absence of a closed form for stable densities, is quite cumbersome, our method allows us to construct estimators reaching the parametric efficiency bounds associated with any prescribed values (α0,b0) of the tail index α and skewness parameter b, while preserving root-n consistency under any (α,b) as well as under usual light-tailed densities. The method furthermore avoids all forms of multidimensional argmin computation. Simulations confirm its excellent finite-sample performances.
Original languageEnglish
Pages (from-to)195-204
JournalJournal of Econometrics
Volume172
Issue number2
DOIs
Publication statusPublished - 2013

Fingerprint

Estimator
Tail index
Skewness
Finite sample
Likelihood estimation
Simulation
Efficiency bounds
Asymmetry
Stable distribution
Least squares

Cite this

Hallin, M. ; Swan, Y. ; Verdebout, T. ; Veredas, D. / One-step R-estimation in linear models with stable errors. In: Journal of Econometrics. 2013 ; Vol. 172, No. 2. pp. 195-204.
@article{6479101d64694c65997e915a31fad978,
title = "One-step R-estimation in linear models with stable errors",
abstract = "Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under α-stable error densities; most of them are not even rate-optimal. In this paper, we propose an original one-step 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 parametric stable-likelihood estimation, due to the absence of a closed form for stable densities, is quite cumbersome, our method allows us to construct estimators reaching the parametric efficiency bounds associated with any prescribed values (α0,b0) of the tail index α and skewness parameter b, while preserving root-n consistency under any (α,b) as well as under usual light-tailed densities. The method furthermore avoids all forms of multidimensional argmin computation. Simulations confirm its excellent finite-sample performances.",
author = "M. Hallin and Y. Swan and T. Verdebout and D. Veredas",
year = "2013",
doi = "10.1016/j.jeconom.2012.08.016",
language = "English",
volume = "172",
pages = "195--204",
journal = "Journal of Econometrics",
issn = "0304-4076",
publisher = "Elsevier BV",
number = "2",

}

Hallin, M, Swan, Y, Verdebout, T & Veredas, D 2013, 'One-step R-estimation in linear models with stable errors', Journal of Econometrics, vol. 172, no. 2, pp. 195-204. https://doi.org/10.1016/j.jeconom.2012.08.016

One-step R-estimation in linear models with stable errors. / Hallin, M.; Swan, Y.; Verdebout, T.; Veredas, D.

In: Journal of Econometrics, Vol. 172, No. 2, 2013, p. 195-204.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - One-step R-estimation in linear models with stable errors

AU - Hallin, M.

AU - Swan, Y.

AU - Verdebout, T.

AU - Veredas, D.

PY - 2013

Y1 - 2013

N2 - Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under α-stable error densities; most of them are not even rate-optimal. In this paper, we propose an original one-step 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 parametric stable-likelihood estimation, due to the absence of a closed form for stable densities, is quite cumbersome, our method allows us to construct estimators reaching the parametric efficiency bounds associated with any prescribed values (α0,b0) of the tail index α and skewness parameter b, while preserving root-n consistency under any (α,b) as well as under usual light-tailed densities. The method furthermore avoids all forms of multidimensional argmin computation. Simulations confirm its excellent finite-sample performances.

AB - Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under α-stable error densities; most of them are not even rate-optimal. In this paper, we propose an original one-step 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 parametric stable-likelihood estimation, due to the absence of a closed form for stable densities, is quite cumbersome, our method allows us to construct estimators reaching the parametric efficiency bounds associated with any prescribed values (α0,b0) of the tail index α and skewness parameter b, while preserving root-n consistency under any (α,b) as well as under usual light-tailed densities. The method furthermore avoids all forms of multidimensional argmin computation. Simulations confirm its excellent finite-sample performances.

U2 - 10.1016/j.jeconom.2012.08.016

DO - 10.1016/j.jeconom.2012.08.016

M3 - Article

VL - 172

SP - 195

EP - 204

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 2

ER -