Flexible modeling based on copulas in nonparametric median regression

Roel Braekers and Ingrid Van Keilegom ()

Journal of Multivariate Analysis, 2009, vol. 100, issue 6, 1270-1281

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.

Keywords: primary; 62G08 secondary; 62G05; 62G20; 62F12; 62E20 Conditional distribution Copulas Empirical processes Median regression Nonparametric regression Quantiles Weak convergence (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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