Rank - Based Inference for Bivariate Extreme - Value

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, rankbased 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 finiteand large-sample performance is then compared to that of their knownmargin analogues, as well as with endpoint-corrected versions thereof. Explicit formulas and consistent estimates for their asymptotic variances are also given.