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Flexible modeling based on copulas in nonparametric median regression

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  • Braekers, Roel
  • Van Keilegom, Ingrid
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    Abstract

    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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    Bibliographic Info

    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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    Related research

    Keywords: primary; 62G08 secondary; 62G05; 62G20; 62F12; 62E20 Conditional distribution Copulas Empirical processes Median regression Nonparametric regression Quantiles Weak convergence;

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    References

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    1. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, 09.
    2. 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.
    3. Einmahl, J.H.J. & Keilegom, I. van, 2008. "Specification tests in nonparametric regression," Open Access publications from Tilburg University urn:nbn:nl:ui:12-192435, Tilburg University.
    4. Ling Hu, 2006. "Dependence patterns across financial markets: a mixed copula approach," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 717-729.
    5. 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.
    6. Adang, P.J.M. & Melenberg , B., 1995. "Nonnegativity constraints and intratemporal uncertainty in multi-good life-cycle models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-383455, Tilburg University.
    7. Einmahl, J.H.J. & Keilegom, I. van, 2006. "Tests for Independence in Nonparametric Regression," Discussion Paper 2006-80, Tilburg University, Center for Economic Research.
    8. 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.
    9. 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.
    10. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
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