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Flexible modeling based on copulas in nonparametric median regression

  • Braekers, Roel
  • Van Keilegom, Ingrid
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    Consider the model Y=m(X)+[epsilon], where m([dot operator])=med(Y[dot operator]) is unknown but smooth. It is often assumed that [epsilon] and X are independent. However, in practice this assumption is violated in many cases. In this paper we propose modeling the dependence between [epsilon] and X by means of a copula model, i.e., where is a copula function depending on an unknown parameter [theta], and F[epsilon] and FX are the marginals of [epsilon] and X. Since many parametric copula families contain the independent copula as a special case, the so-obtained regression model is more flexible than the 'classical' regression model. We estimate the parameter [theta] via a pseudo-likelihood method and prove the asymptotic normality of the estimator, based on delicate empirical process theory. We also study the estimation of the conditional distribution of Y given X. The procedure is illustrated by means of a simulation study, and the method is applied to data on food expenditures in households.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 100 (2009)
    Issue (Month): 6 (July)
    Pages: 1270-1281

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    Handle: RePEc:eee:jmvana:v:100:y:2009:i:6:p:1270-1281
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    1. Einmahl, J.H.J. & van Keilegom, I., 2008. "Specification tests in nonparametric regression," Other publications TiSEM 2c94c2d8-8305-4fb1-b47f-7, Tilburg University, School of Economics and Management.
    2. Xiaohong Chen & Oliver Linton & Ingred Van Keilegom, 2002. "Estimation of semiparametric models when the criterion function is not smooth," CeMMAP working papers CWP02/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Einmahl, J.H.J. & van Keilegom, I., 2006. "Tests for Independence in Nonparametric Regression," Discussion Paper 2006-80, Tilburg University, Center for Economic Research.
    4. Scaillet, Olivier, 2007. "Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 533-543, March.
    5. repec:cep:stiecm:/2003/450 is not listed on IDEAS
    6. Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2004. "Efficient Estimation of Semiparametric Multivariate Copula Models," Vanderbilt University Department of Economics Working Papers 0420, Vanderbilt University Department of Economics.
    7. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    8. Ling Hu, 2006. "Dependence patterns across financial markets: a mixed copula approach," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 717-729.
    9. Charpentier, Arthur & Segers, Johan, 2007. "Lower tail dependence for Archimedean copulas: Characterizations and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 525-532, May.
    10. Chen, Xiaohong & Fan, Yanqin, 2007. "A Model Selection Test For Bivariate Failure-Time Data," Econometric Theory, Cambridge University Press, vol. 23(03), pages 414-439, June.
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