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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521845731, October.
- 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.
- 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.
- 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.
- Bantli, Faouzi El & Hallin, Marc, 1999. "L1-estimation in linear models with heterogeneous white noise," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 305-315, December.
- 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
- Blattberg, Robert & Sargent, Thomas J, 1971. "Regression with Non-Gaussian Stable Disturbances: Some Sampling Results," Econometrica, Econometric Society, vol. 39(3), pages 501-510, May.
- Allal, Jelloul & Kaaouachi, Abdelali & Paindaveine, Davy, 2001. "R-estimation for ARMA models," MPRA Paper 21167, University Library of Munich, Germany.
- Knight, Keith, 1998. "Bootstrapping sample quantiles in non-regular cases," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 259-267, March.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:172:y:2013:i:2:p:195-204. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.