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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.

Suggested Citation

  • 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, 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.
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    1. Bouezmarni, Taoufik & Rombouts, Jeroen V.K. & Taamouti, Abderrahim, 2010. "Asymptotic properties of the Bernstein density copula estimator for [alpha]-mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 1-10, January.

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