Consider a continuous random pair (X, Y) whose dependence is characterized by an extreme-value copula with Pickands dependence function A. When the marginal distributions of X and Y are known, several consistent estimators of A are available. Most of them are variants of the estimators due to Pickands [Bull. Inst. Internat. Statist. 49 (1981) 859–878] and Capéraà, Fougères and Genest [Biometrika 84 (1997) 567–577]. In this paper, rank-based versions of these estimators are proposed for the more common case where the margins of X and Y are unknown. Results on the limit behavior of a class of weighted bivariate empirical processes are used to show the consistency and asymptotic normality of these rank-based estimators. Their finite- and large-sample performance is then compared to that of their known-margin analogues, as well as with endpoint-corrected versions thereof. Explicit formulas and consistent estimates for their asymptotic variances are also given.
@article{1247836675,
author = {Genest, Christian and Segers, Johan},
title = {Rank-based inference for bivariate extreme-value copulas},
journal = {Ann. Statist.},
volume = {37},
number = {1},
year = {2009},
pages = { 2990-3022},
language = {en},
url = {http://dml.mathdoc.fr/item/1247836675}
}
Genest, Christian; Segers, Johan. Rank-based inference for bivariate extreme-value copulas. Ann. Statist., Tome 37 (2009) no. 1, pp. 2990-3022. http://gdmltest.u-ga.fr/item/1247836675/