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Finite-sample distribution-free inference in linear median regressions under heteroscedasticity and non-linear dependence of unknown form

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  • Elise Coudin
  • Jean-Marie Dufour

Abstract

We construct finite-sample distribution-free tests and confidence sets for the parameters of a linear median regression, where no parametric assumption is imposed on the noise distribution. The set-up studied allows for non-normality, heteroscedasticity, non-linear serial dependence of unknown forms as well as for discrete distributions. We consider a mediangale structure--the median-based analogue of a martingale difference--and show that the signs of mediangale sequences follow a nuisance-parameter-free distribution despite the presence of non-linear dependence and heterogeneity of unknown form. We point out that a simultaneous inference approach in conjunction with sign transformations yield statistics with the required pivotality features--in addition to usual robustness properties. Monte Carlo tests and projection techniques are then exploited to produce finite-sample tests and confidence sets. Further, under weaker assumptions, which allow for weakly exogenous regressors and a wide class of linear dependence schemes in the errors, we show that the procedures proposed remain asymptotically valid. The regularity assumptions used are notably less restrictive than those required by procedures based on least absolute deviations (LAD). Simulation results illustrate the performance of the procedures. Finally, the proposed methods are applied to tests of the drift in the Standard and Poor's composite price index series (allowing for conditional heteroscedasticity of unknown form). Copyright (C) The Author(s). Journal compilation (C) Royal Economic Society 2009

Suggested Citation

  • Elise Coudin & Jean-Marie Dufour, 2009. "Finite-sample distribution-free inference in linear median regressions under heteroscedasticity and non-linear dependence of unknown form," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 19-49, January.
  • Handle: RePEc:ect:emjrnl:v:12:y:2009:i:s1:p:s19-s49
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    Cited by:

    1. Khalaf, Lynda & Saunders, Charles J., 2017. "Monte Carlo forecast evaluation with persistent data," International Journal of Forecasting, Elsevier, vol. 33(1), pages 1-10.
    2. 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)," Discussion Paper 2011-002, Tilburg University, Center for Economic Research.
    3. Luger, Richard, 2012. "Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3198-3211.
    4. Elise Coudin & Jean-Marie Dufour, 2010. "Finite and Large Sample Distribution-Free Inference in Median Regressions with Instrumental Variables," Working Papers 2010-56, Center for Research in Economics and Statistics.
    5. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2532-2553, November.
    6. Gossner, Olivier & Schlag, Karl H., 2013. "Finite-sample exact tests for linear regressions with bounded dependent variables," Journal of Econometrics, Elsevier, vol. 177(1), pages 75-84.
    7. Chen, Min & Zhu, Ke, 2014. "Sign-based specification tests for martingale difference with conditional heteroscedasity," MPRA Paper 56347, University Library of Munich, Germany.
    8. Oliver Gossner & Karl Schlag, 2012. "Finite Sample Exact tests for Linear," Vienna Economics Papers 1201, University of Vienna, Department of Economics.

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