Semiparametric estimation of conditional copulas

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• 作者：Fentaw Abegaz^a ; ^b ; Irè ; ne Gijbels^b ; ^{irene.gijbels@wis.kuleuven.be} ; Noë ; l Veraverbeke^c
• 关键词：62H12 ; 62H20 ; 62G08 ; 62G20 ; 62E20
• 刊名：Journal of Multivariate Analysis
• 出版年：2012
• 期刊代码：77_0047259x
• 类别：mt
• 出版时间：September, 2012
• 卷：110
• 期：Complete
• 页码：43-73
• 文件大小：621 K

摘要

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.