Inference for the limiting cluster size distribution of extreme values
| Autor: | Christian Y. Robert |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences limiting cluster size distribution 60G70 Extreme values extremal index Poisson distribution Statistics - Applications Point process 62M09 Methodology (stat.ME) symbols.namesake Cluster (physics) Range (statistics) Applications (stat.AP) Statistical physics Extreme value theory Statistics - Methodology 62G20 Mathematics 62E20 Estimator strictly stationary sequences exceedance point processes Stationary sequence symbols Probability distribution Statistics Probability and Uncertainty 60G70 62E20 62M09 (Primary) 62G20 62G32 (Secondary) 62G32 |
| Zdroj: | Ann. Statist. 37, no. 1 (2009), 271-310 |
| Popis: | Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The underlying Poisson points represent the cluster positions and the multiplicities correspond to the cluster sizes. In the present paper we introduce estimators of the limiting cluster size probabilities, which are constructed through a recursive algorithm. We derive estimators of the extremal index which plays a key role in determining the intensity of cluster positions. We study the asymptotic properties of the estimators and investigate their finite sample behavior on simulated data. Comment: Published in at http://dx.doi.org/10.1214/07-AOS551 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|