STATISTICS FOR NEAR INDEPENDENCE IN MULTIVARIATE EXTREME VALUES

We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing tec hniques when the variables are near independence. We examine inference under the model and develop tests for independence of extremes of the marginal variables, both when the thresholds are fixed, and when they increase with the sample size. Motivated by results obtained from thi s model, we give a new and widely applicable characterisation of depen dence in the joint tail which includes existing models as special case s. A new parameter which governs the form of dependence is of fundamen tal importance to this characterisation. By estimating this parameter, we develop a diagnostic test which assesses the applicability of biva riate extreme value joint tail models. The methods are demonstrated th rough simulation and by analysing two previously published data sets.