Estimation of a Conditional Copula and Association Measures

Authors


Irène Gijbels, Department of Mathematics and Leuven Statistics Research Center (LStat), Katholieke Universiteit Leuven, Celestijnenlaan 200B, Box 2400, B-3001 Leuven (Heverlee), Belgium.
E-mail: irene.gijbels@wis.kuleuven.be

Abstract

Abstarct.  This paper is concerned with studying the dependence structure between two random variables Y1 and Y2 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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