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Finite-sample Distribution-free Inference in Linear Median Regression under Heteroskedasticity and Nonlinear Dependence of Unknown Form

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  • Elise Coudin

    (Crest)

  • Jean-Marie Dufour

    (Crest)

Abstract

We construct finite-sample distribution-free tests and confidence sets for the parametersof a linear median regression where no parametric assumptions are imposed on thenoise distribution. The setup we consider allows for nonnormality, heteroskedasticityand nonlinear serial dependence in the errors. Such semiparametric models are usuallyanalyzed using only asymptotically justified approximate methods, which can be arbitrarilyunreliable in finite samples. We consider first the property of mediangale – themedian-based analogue of a martingale difference – and show that the signs of mediangalesequences follow a nuisance-parameter free-distribution despite the presence ofnonlinear dependence and heterogeneity of unknown form. We point out that a simultaneousinference approach in conjunction with sign transformations do provide statisticswith the required pivotality features – in addition to usual robustness properties. Thosesign-based statistics are exploited – usingMonte Carlo tests and projection techniques –in order to produce valid inference in finite samples. An asymptotic theory which holdsunder weaker assumptions is also provided. Finally, simulation results illustrating theperformance and two applications are presented.

Suggested Citation

  • Elise Coudin & Jean-Marie Dufour, 2007. "Finite-sample Distribution-free Inference in Linear Median Regression under Heteroskedasticity and Nonlinear Dependence of Unknown Form," Working Papers 2007-38, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2007-38
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    1. repec:hal:journl:peer-00834424 is not listed on IDEAS
    2. Taamouti, Abderrahim & Dufour, Jean-Marie, 2008. "Exact optimal and adaptive inference in regression models under heteroskedasticity and non-normality of unknown forms," UC3M Working papers. Economics we086027, Universidad Carlos III de Madrid. Departamento de Economía.
    3. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2010. "Asset-pricing anomalies and spanning: Multivariate and multifactor tests with heavy-tailed distributions," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 763-782, September.
    4. Élise, COUDIN & Jean-Marie DUFOUR, 2017. "Finite-Sample Generalized Confidence Distributions and Sign-Based Robust Estimators in Median Regressions with Heterogeneous Dependent Errors," Cahiers de recherche 01-2017, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    5. 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.
    6. Alex Maynard, 2006. "The forward premium anomaly: statistical artefact or economic puzzle? New evidence from robust tests," Canadian Journal of Economics, Canadian Economics Association, vol. 39(4), pages 1244-1281, November.

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