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Flexible modeling based on copulas in nonparametric median regression

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  • Braekers, Roel
  • Van Keilegom, Ingrid

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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  • Braekers, Roel & Van Keilegom, Ingrid, 2009. "Flexible modeling based on copulas in nonparametric median regression," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1270-1281, July.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:6:p:1270-1281
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    References listed on IDEAS

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    1. Einmahl, John H.J. & Van Keilegom, Ingrid, 2008. "Specification tests in nonparametric regression," Journal of Econometrics, Elsevier, vol. 143(1), pages 88-102, March.
    2. Chen, Xiaohong & Fan, Yanqin, 2007. "A Model Selection Test For Bivariate Failure-Time Data," Econometric Theory, Cambridge University Press, vol. 23(3), pages 414-439, June.
    3. 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.
    4. 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, September.
    5. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
    6. Einmahl, J.H.J. & van Keilegom, I., 2006. "Tests for Independence in Nonparametric Regression," Other publications TiSEM 0c6f2c43-aa7d-45c1-9d43-7, Tilburg University, School of Economics and Management.
    7. Adang, Pim & Melenberg, Bertrand, 1995. "Nonnegativity Constraints and Intratemporal Uncertainty in a Multi-good Life-Cycle Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(1), pages 1-15, Jan.-Marc.
    8. 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.
    9. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
    10. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    11. Ling Hu, 2006. "Dependence patterns across financial markets: a mixed copula approach," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 717-729.
    12. 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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