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Estimation of a Conditional Copula and Association Measures
Author(s) -
VERAVERBEKE NOËL,
OMELKA MAREK,
GIJBELS IRÈNE
Publication year - 2011
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2011.00744.x
Subject(s) - copula (linguistics) , mathematics , covariate , estimator , econometrics , statistics , conditional dependence , conditional probability distribution , conditional expectation , parametric statistics , conditional independence
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.