Test d`indépendance pour les coppules

A new test procedure of independence in
Copula models via χ2-divergence
Salim BOUZEBDA and Amor KEZIOU a,b
a L.S.T.A.-Université
Paris 6, 175, rue du Chevaleret, Boı̂te 158, 75013 Paris.
[email protected]
b LSTA-Université
Paris 6, UMR 6056 CNRS et Université de Reims
Champagne-Ardenne UFR Sciences, Moulin de la Housse, B.P. 1039 F-51687
Reims.
[email protected]
Abstract
The purpose of this paper is to provide limit laws for semi-parametric estimators of
copulas. Some new statistical tests of independence are introduced as a consequence
of this methodology. We are primarily concerned with the case where the parameter
lies on the boundary of the admissible domain, and introduce a new method to cope
with this case.
Key words: Dependence function; Gumbel copula; pseudo-likelihood; Asymptotic
theory; Multivariate rank statistic; Semiparametric inference.