Statistics for near independence in multivariate extreme values. (English) Zbl 0865.62040

Ledford, Anthony W.; Tawn, Jonathan A.

Biometrika 83, No. 1, 169-187 (1996).

Summary: We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques 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 this model, we give a new and widely applicable characterization of dependence in the joint tail which includes existing models as special cases. A new parameter which governs the form of dependence is of fundamental importance to this characterization. By estimating this parameter, we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models. The methods are demonstrated through simulation and by analyzing two previously published data sets.

MSC:

62H12	Estimation in multivariate analysis
62E20	Asymptotic distribution theory in statistics
62H99	Multivariate analysis

Keywords:

asymptotic independence; coefficient of tail dependence; generalized Pareto distribution; maximum likelihood; nonregular estimation; Poisson process; threshold exceedance; multivariate extreme value threshold model; joint tail estimation; near independence; tests for independence of extremes; marginal variables; characterization of dependence; diagnostic test; simulation