Estimation of a Conditional Copula and Association Measures |
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| Authors: | NOËL VERAVERBEKE MAREK OMELKA IRÈNE GIJBELS |
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| Institution: | 1. Center for Statistics, Hasselt University;2. Department of Probability and Statistics, Faculty of Mathematics and Physics, Charles University Prague;3. Department of Mathematics and Leuven Statistics Research Center (LStat), Katholieke Universiteit Leuven |
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| Abstract: | Abstarct. This paper is concerned with studying the dependence structure between two random variables Y 1 and Y 2 conditionally upon a covariate X. The dependence structure is modelled via a copula function, which depends on the given value of the covariate in a general way. Gijbels et al. (Comput. Statist. Data Anal., 55, 2011, 1919) suggested two non‐parametric estimators of the ‘conditional’ copula and investigated their numerical performances. In this paper we establish the asymptotic properties of the proposed estimators as well as conditional association measures derived from them. Practical recommendations for their use are then discussed. |
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| Keywords: | asymptotic representation conditional Kendall's tau empirical copula process fixed design random design smoothing weak convergence |
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