One-step R-estimation in linear models with stable errors
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.
References listed on IDEAS
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- Marc Hallin & Yves-Caoimhin Swan & Thomas Verdebout & David Veredas, 2011. "Rank-based testing in linear models with stable errors," ULB Institutional Repository 2013/136196, ULB -- Universite Libre de Bruxelles.
- repec:ulb:ulbeco:2013/136280 is not listed on IDEAS
- Bantli, Faouzi El & Hallin, Marc, 1999.
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Statistics & Probability Letters,
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- Marc Hallin & Faouzi El Bantli, 1999. "L1-estimation in linear models with heterogeneous white noise," ULB Institutional Repository 2013/2083, ULB -- Universite Libre de Bruxelles.
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- Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, August.
- Deo, Rohit S., 2002. "On testing the adequacy of stable processes under conditional heteroscedasticity," Journal of Empirical Finance, Elsevier, vol. 9(2), pages 257-270, March.
- Knight, Keith, 1998. "Bootstrapping sample quantiles in non-regular cases," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 259-267, March.
- Allal, Jelloul & Kaaouachi, Abdelali & Paindaveine, Davy, 2001. "R-estimation for ARMA models," MPRA Paper 21167, University Library of Munich, Germany.
- Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November. Full references (including those not matched with items on IDEAS)
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