Name
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 Caperaa-Fougeres-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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.jmva.2010.07.011 | J. Multivariate Analysis |
Keywords | Field | DocType |
unit simplex,multivariate distribution,linear regression,minimum-variance estimator,ordinary least-squares estimator,62h20,60f17,joint asymptotic distribution,empirical process,arbitrary dimension,pickands,multivariate extreme-value distribution,asymptotic distribution,pickands dependence function,extreme-value copula,caperaa-fougeres-genest estimator,convex function,ordinary least squares,dependence function,random function,62g32,nonparametric estimation,ordinary least square,extreme value,weight function,multivariate analysis,value function,linear regression model,minimum variance,random sampling,asymptotic behavior,satisfiability,extreme value distribution | Econometrics,Joint probability distribution,Multivariate normal distribution,Variance function,Statistics,Real-valued function,Mathematics,Marginal distribution,Estimator,Random function,Asymptotic distribution | Journal |
Volume | Issue | ISSN |
102 | 1 | Journal of Multivariate Analysis |
Citations | PageRank | References |
4 | 0.72 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gordon Gudendorf | 1 | 4 | 0.72 |
| Johan Segers | 2 | 41 | 10.37 |