61134

Автор(ов): 

1

Параметры публикации
Тип публикации: 
Статья в журнале/сборнике
Название: 
Threshold selection for extremal index estimation
ISBN/ISSN: 
2194-1009
DOI: 
10.1007/978-3-030-57306-5_31
Наименование источника: 
Nonparametric Statistics, Springer Proceedings in Mathematics & Statistics
Обозначение и номер тома: 
339
Город: 
Salerno
Издательство: 
Springer
Год издания: 
2020
Страницы: 
341– 356
Аннотация
We consider the nonparametric estimation of the extremal index of stochastic processes. The discrepancy method that was proposed by the author as a data-driven smoothing tool for probability density function estimation is extended to find a threshold parameter u for an extremal index estimator in case of heavy-tailed distributions. To this end, the discrepancy statistics are based on the von Mises– Smirnov statistic and the k largest order statistics instead of an entire sample. The asymptotic chi-squared distribution of the discrepancy measure is derived. Its quan8 tiles may be used as discrepancy values. An algorithm to select u for an estimator of the extremal index is proposed. The accuracy of the discrepancy method is checked by a simulation study.
Библиографическая ссылка: 
Маркович Н.М. Threshold selection for extremal index estimation // Nonparametric Statistics, Springer Proceedings in Mathematics & Statistics. 2020. 339. С. 341– 356.