Efficient estimation of the canonical dependence function
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.
scientific article; zbMATH DE number 2118667