Flexible modeling based on copulas in nonparametric median regression

Braekers, Roel;Van Keilegom, Ingrid
(2007) , 21 pages

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Consider the model Y = m(X ) + ε, where m(·) = med(Y|·) is unknown but smooth. It is often assumed that ε and X are independent. However, in practice this assumption is in many cases violated. In this paper we propose to model the dependence between ε and X by means of a copula model, i.e. (ε,X)∼Cθ(Fε (·), FX(·)), where Cθ is a copula function depending on an unknown parameter θ, and Fε and FX are the marginals of ε 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 θ 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, R., & Van Keilegom, I. (2007). Flexible modeling based on copulas in nonparametric median regression (STAT Discussion Paper 0724). https://hdl.handle.net/2078.5/35067