Semiparametric estimation of conditional copulas

Fentaw Abegaz, Irène Gijbels and Noël Veraverbeke

Journal of Multivariate Analysis, 2012, vol. 110, issue C, 43-73

Abstract: The manner in which two random variables influence one another often depends on covariates. A way to model this dependence is via a conditional copula function. This paper contributes to the study of semiparametric estimation of conditional copulas by starting from a parametric copula function in which the parameter varies with a covariate, and leaving the marginals unspecified. Consequently, the unknown parts in the model are the parameter function and the unknown marginals. The authors use a local pseudo-likelihood with nonparametrically estimated marginals approximating the unknown parameter function locally by a polynomial. Under this general setting, they prove the consistency of the estimators of the parameter function as well as its derivatives; they also establish asymptotic normality. Furthermore, they derive an expression for the theoretical optimal bandwidth and discuss practical bandwidth selection. They illustrate the performance of the estimation procedure with data-driven bandwidth selection via a simulation study and a real-data case.

Keywords: Asymptotic normality; Conditional copula; Consistency; Local polynomial fitting; Semiparametric estimation (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (17)

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DOI: 10.1016/j.jmva.2012.04.001

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