Abstract
AbstractA 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 paper investigates the large-sample behavior of a nonparametric estimator of this function due to Cormier et al. (Extremes 17:633–659, 2014). These authors showed how to construct this estimator through constrained quadratic median B-spline smoothing of pairs of pseudo-observations derived from a random sample. Their estimator is shown here to exist whatever the order $$m \ge 3$$
m
≥
3
of the B-spline basis, and its consistency is established under minimal conditions. The large-sample distribution of this estimator is also determined under the additional assumption that the underlying Pickands dependence function is a B-spline of given order with a known set of knots.
Funder
Natural Sciences and Engineering Research Council of Canada
Canada Research Chairs
Canadian Statistical Sciences Institute
Deutsche Forschungsgemeinschaft
Trottier Institute for Science and Public Policy
Publisher
Springer Science and Business Media LLC
Subject
Economics, Econometrics and Finance (miscellaneous),Engineering (miscellaneous),Statistics and Probability
Reference37 articles.
1. Berghaus, B., Bücher, A.: Goodness-of-fit tests for multivariate copula-based time series models. Econom. Theory 33, 292–330 (2017)
2. Berghaus, B., Bücher, A., Dette, H.: Minimum distance estimators of the Pickands dependence function and related tests of multivariate extreme-value dependence. J. SFdS 154, 116–137 (2013)
3. Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1968)
4. Bücher, A., Dette, H., Volgushev, S.: New estimators of the Pickands dependence function and a test for extreme-value dependence. Ann. Statist. 39, 1963–2006 (2011)
5. Capéraà, P., Fougères, A.-L., Genest, C.: A nonparametric estimation procedure for bivariate extreme value copulas. Biometrika 84, 567–577 (1997)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献