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

Marc Hallin (), Yvik Swan, Thomas Verdebout and David Veredas

Journal of Econometrics, 2013, vol. 172, issue 2, 195-204

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.

Keywords: Stable distributions; Local asymptotic normality; LAD estimation; R-estimation; Asymptotic relative efficiency (search for similar items in EconPapers)
Date: 2013
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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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