Using B-splines for nonparametric inference on bivariate extreme-value copulas

Abstract

A visual tool is proposed for detecting the presence of extreme-value dependence or extremal tail behavior in bivariate data. The points appearing on the plot stem from rank-based transformations of the observations and can serve to estimate the unknown Pickands dependence function of the underlying extreme-value copula or its attractor. Quadratic constrained B-spline smoothing is used to derive an intrinsic estimator, which naturally leads to a test of extremeness. Both the estimator and the test are seen to perform well in simulations. The proposed methodology is illustrated with real data and the treatment of ties is briefly discussed.