Multivariate extremes over a random number of observations
| Autor: | Simone A. Padoan, Enkelejd Hashorva, Stefano Rizzelli |
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| Předmět: |
Statistics and Probability
FOS: Computer and information sciences extreme-value copula Multivariate statistics pickands dependence function EXTREMAL DEPENDENCE EXTREME-VALUE COPULA INVERSE PROBLEM MULTIVARIATE MAX-STABLE DISTRIBUTION NONPARAMETRIC ESTIMATION PICKANDS DEPENDENCE FUNCTION Inverse transform sampling 01 natural sciences Unobservable Methodology (stat.ME) 010104 statistics & probability multivariate max-stable distribution 0502 economics and business Attractor Limit (mathematics) Statistical physics 0101 mathematics Statistics - Methodology 050205 econometrics Mathematics inference 05 social sciences Estimator extremal dependence nonparametric estimation dependence Inverse problem 60G70 62G32 Settore SECS-S/01 - STATISTICA inverse problem Statistics Probability and Uncertainty Maxima nonparametric-estimation |
| Popis: | The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated data, such as maxima of a random number of observations, are considered. We derive a limit theorem concerning the attractors for the distributions of the aggregated data, which boil down to a new family of max-stable distributions. We also connect the extremal dependence structure of classical max-stable distributions and that of our new family of max-stable distributions. By means of an inversion method, we derive a semiparametric composite-estimator for the extremal dependence of the unobservable data, starting from a preliminary estimator of the extremal dependence of the aggregated data. Furthermore, we develop the large-sample theory of the composite-estimator and illustrate its finite-sample performance via a simulation study. |
| Databáze: | OpenAIRE |
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