Nonparametric estimation of an extreme-value copula in arbitrary dimensions

Gordon Gudendorf and Johan Segers

Journal of Multivariate Analysis, 2011, vol. 102, issue 1, 37-47

Abstract: Inference on an extreme-value copula usually proceeds via its Pickands dependence function, which is a convex function on the unit simplex satisfying certain inequality constraints. In the setting of an i.i.d. random sample from a multivariate distribution with known margins and an unknown extreme-value copula, an extension of the Capéraà-Fougères-Genest estimator was introduced by D. Zhang, M. T. Wells and L. Peng [Nonparametric estimation of the dependence function for a multivariate extreme-value distribution, Journal of Multivariate Analysis 99 (4) (2008) 577-588]. The joint asymptotic distribution of the estimator as a random function on the simplex was not provided. Moreover, implementation of the estimator requires the choice of a number of weight functions on the simplex, the issue of their optimal selection being left unresolved. A new, simplified representation of the CFG-estimator combined with standard empirical process theory provides the means to uncover its asymptotic distribution in the space of continuous, real-valued functions on the simplex. Moreover, the ordinary least-squares estimator of the intercept in a certain linear regression model provides an adaptive version of the CFG-estimator whose asymptotic behavior is the same as if the variance-minimizing weight functions were used. As illustrated in a simulation study, the gain in efficiency can be quite sizable.

Keywords: Empirical; process; Linear; regression; Minimum-variance; estimator; Multivariate; extreme-value; distribution; Ordinary; least; squares; Pickands; dependence; function; Unit; simplex (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (6)

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