Efficient estimation of the canonical dependence function
type: Item
instance of: scholarly article
title: Efficient estimation of the canonical dependence function
zbMATH Open document ID: 1053.62062
DOI: 10.1023/A:1026229314063
author: Michael Falk
author: Rolf-Dieter Reiss
published in: Extremes
publication date: 2004-11-24T00:00:00Z
review text: Any bivariate max-stable (extreme value) distribution \(G\) with reversed standard exponential margins can be represented in the form \[ G(x,y)=\exp ( (x+y) D(y/(x+y))),\quad x,y<0, \] where \(D:[0,1]\to[0,1]\) is the Pickands dependence function. The function \(\vartheta(t)=(1-D(z))/\min(z,1-z)\) is called the canonical dependence function. The problem is to estimate \(D\) and \(\vartheta\) by i.i.d. observations from \(G\). Local asymptotic normality of the loglikelihood function of \(r\times r\) table sorting is demonstrated. Asymptotically normal and efficient estimators are constructed.
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 62H20
zbMATH DE Number: 2118667
zbMATH Keywords: bivariate extreme value distribution
zbMATH Keywords: Pickands representation
zbMATH Keywords: local asymptotic normality (LAN)
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2118667