Semiparametric estimation of conditional copulas

  • Authors:

  • Fentaw Abegaz;IrèNe Gijbels;NoëL Veraverbeke

  • Affiliations:

  • Addis Ababa University, Ethiopia and Department of Mathematics, and Leuven Statistics Research Center (LStat), Katholieke Universiteit Leuven, Belgium;Department of Mathematics, and Leuven Statistics Research Center (LStat), Katholieke Universiteit Leuven, Belgium;Center for Statistics, Universiteit Hasselt, Belgium

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2012

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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.