Strong convergence of multivariate point processes of exceedances

DOI10.1007/BF00773345zbMath0802.60045MaRDI QIDQ1335343

Rolf-Dieter Reiss, Edgar Kaufmann

Publication date: 4 October 1994

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

upper boundsPoisson processmultivariate point processesvariational distanceexceedances of random thresholdsstrong convergence of multivariate maximatriangular scheme of random vectors

Mathematics Subject Classification ID

Strong limit theorems (60F15) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (8)

Approximation rates for multivariate exceedances ⋮ Strong convergence of multivariate maxima ⋮ Testing for a multivariate generalized Pareto distribution ⋮ Peaks-over-threshold stability of multivariate generalized Pareto distributions ⋮ Estimation of canonical dependence parameters in a class of bivariate peaks-over-threshold models ⋮ Estimating the index of a stable law via the pot-method ⋮ Efficient estimators and LAN in canonical bivariate POT models. ⋮ A characterization of the rate of convergence in bivariate extreme value models

Cites Work

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• Rates of convergence in multivariate extreme value theory
• Approximate distributions of order statistics. With applications to nonparametric statistics
• Poisson approximation of empirical processes
• Statistical inference using extreme order statistics
• max-infinitely divisible and max-stable sample continuous processes
• Max-infinite divisibility

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