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

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Author Info

  • Hallin, Marc
  • Swan, Yvik
  • Verdebout, Thomas
  • Veredas, David

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 172 (2013)
Issue (Month): 2 ()
Pages: 195-204

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Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:195-204

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Stable distributions; Local asymptotic normality; LAD estimation; R-estimation; Asymptotic relative efficiency;

References

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  1. 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.
  2. Allal, Jelloul & Kaaouachi, Abdelali & Paindaveine, Davy, 2001. "R-estimation for ARMA models," MPRA Paper 21167, University Library of Munich, Germany.
  3. 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.
  4. Knight, Keith, 1998. "Bootstrapping sample quantiles in non-regular cases," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 259-267, March.
  5. Yves Dominicy & David Veredas, 2013. "The method of simulated quantiles," ULB Institutional Repository 2013/136280, ULB -- Universite Libre de Bruxelles.
  6. Blattberg, Robert & Sargent, Thomas J, 1971. "Regression with Non-Gaussian Stable Disturbances: Some Sampling Results," Econometrica, Econometric Society, vol. 39(3), pages 501-10, May.
  7. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  8. 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.
  9. 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.
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Cited by:
  1. Nolan, John P. & Ojeda-Revah, Diana, 2013. "Linear and nonlinear regression with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 186-194.
  2. Mikosch, Thomas & de Vries, Casper G., 2013. "Heavy tails of OLS," Journal of Econometrics, Elsevier, vol. 172(2), pages 205-221.

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