Title: Asymptotic behavior of an intrinsic rank-based estimator of the Pickands dependence function constructed from B-splines
Authors: Christian Genest - McGill University (Canada) [presenting]
Abstract: A bivariate extreme-value copula is characterized by its Pickands dependence function, i.e., a convex function defined on the unit interval satisfying boundary conditions. This function has been the object of intense study over the past thirty years, and several rank-based estimators thereof are available in the literature. The large-sample behavior of one such estimator is discussed. This estimator is constructed from B-splines and has the advantage of being intrinsic. Under the assumption that the Pickands dependence function is a linear combination of B-splines of order 3 or 4 with a given set of knots, the vector of coefficients is estimated by a constrained penalized minimum distance method. The asymptotic behavior of this estimator will be presented and used to deduce the weak limit of the resulting Pickands dependence function, spectral distribution, and spectral density.