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

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    Publication type
    Journal article
    Author
    Hallin, Marc
    Swan, Yvik
    Verdebout, Thomas
    Veredas, David
    Publication Year
    2013
    Journal
    Journal of Econometrics
    Publication Volume
    172
    Publication Issue
    2
    Publication Begin page
    195
    Publication End page
    204
    
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    Abstract
    Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under -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- 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 of the tail index and skewness parameter , while preserving root- consistency under any 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.
    Keyword
    Stable Distributions, Local Asymptotic Normality, LAD Estimation, R-Estimation, Asymptotic Relative Efficiency
    Knowledge Domain/Industry
    Accounting & Finance
    DOI
    10.1016/j.jeconom.2012.08.016
    URI
    http://hdl.handle.net/20.500.12127/5222
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jeconom.2012.08.016
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