Testing the independence of maxima: from bivariate vectors to spatial extreme fields: asymptotic independence of extremes (Q549643)

Let \(Z\) be a stationary isotropic random field with a marginal distribution \(F\). The authors propose to use the (normalized) madogam \( \nu_Z(h)=2^{-1}\mathbf {E}| F(Z(s+h))-F(Z(s))|\) to analyze the asymptotic independence of extremes for \(Z(0)\) and \(Z(h)\) at fixed \(h\). Some empirical versions of the madogram are considered for single and multiple realizations problems. Properties of the obtained statistics are investigated via simulations. Applications to climatological data on temperature and precipitation are presented.