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Rank-based testing in linear models with stable errors

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

Abstract

Linear models with stable error densities are considered, and their local asymptotic normality with respect to the regression parameter is established. We use this result, combined with Le Cam's third lemma, to obtain local powers and asymptotic relative efficiencies for various classical rank tests (the regression and analysis of variance counterparts of the Wilcoxon, van der Waerden and median tests) under α-stable densities with various values of the skewness parameter and tail index. The same results are used to construct new rank tests, based on ‘stable scores’, achieving parametric optimality at specified stable densities. A Monte Carlo study is conducted to compare their finite-sample relative performances.

Suggested Citation

  • Marc Hallin & Yvik Swan & Thomas Verdebout & David Veredas, 2011. "Rank-based testing in linear models with stable errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 305-320.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:305-320
    DOI: 10.1080/10485252.2010.525234
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    Cited by:

    1. Hallin, Marc & Swan, Yvik & Verdebout, Thomas & Veredas, David, 2013. "One-step R-estimation in linear models with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 195-204.
    2. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, Institute of Labor Economics (IZA).
    3. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2011. "A class of simple distribution-free rank-based unit root tests," Journal of Econometrics, Elsevier, vol. 163(2), pages 200-214, August.
    4. repec:hal:journl:peer-00834424 is not listed on IDEAS
    5. Hallin, M. & van den Akker, R. & Werker, B.J.M., 2011. "A Class of Simple Distribution-free Rank-based Unit Root Tests (Revision of DP 2010-72)," Other publications TiSEM 004c9726-ec6a-4884-8238-d, Tilburg University, School of Economics and Management.
    6. Pupashenko, Daria & Ruckdeschel, Peter & Kohl, Matthias, 2015. "L2 differentiability of generalized linear models," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 155-164.

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