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Автор(ов): 

1

Параметры публикации
Тип публикации: 
Тезисы доклада
Название: 
Nonparametric estimation of extremal index with smoothing
ISBN/ISSN: 
978-88-61970-00-7
Наименование конференции: 
4th Conference of the International Society for Nonparametric Statistics (ISNPS 2018, Salerno, Italy)
Наименование источника: 
Book of Abstracts of the 4th Conference of the International Society for Nonparametric Statistics (ISNPS 2018, Salerno, Italy)
Город: 
Salerno
Издательство: 
Creative Commons CC BY-NC-ND 4.0 License
Год издания: 
2018
Страницы: 
79-80
Аннотация
We consider the nonparametric estimation of extremal index of stochastic processes. There are nonparametric methods like well-known blocks, runs and intervals estimators of the extremal index which all require the selection of an appropriate threshold u. Some modifications of blocks estimator (see, \cite{Drees-2011}) require the block size without u. In order to estimate u %a unknown parameter we develop the approach based on the discrepancy method. The latter was proposed first for a nonparametric estimation of probability density functions %\cite{Markovich-89}, \cite{Vapnik}. The discrepancy statistics based on the von Mises-Smirnov's (M-S) and the Kolmogorov-Smirnov (K-S) statistics were used as the discrepancy measures and some quantiles of limit distributions of M-S and K-S statistics were used as the discrepancy value $\delta$. The method was modified by the author for heavy-tailed densities \cite{Markovich-2016} and the extremal index \cite{Markovich-2015}. To this end, the discrepancy statistics M-S and K-S were calculated not by entire sample but only by K largest order statistics. The selection of K and $\delta$ is still an open problem. To overcome this problem we obtain now the limit distribution of the modified M-S statistic regarding the value K. This allows us to select $\delta$ using quantiles of the latter distribution. To this aim, we use the exponential limit distribution of the normalized inter-cluster size derived in \cite{Ferro}. The cluster means the number of consecutive observations exceeding threshold u between two consecutive nonexceedances. The exposition is accompanying by simulated examples.
Библиографическая ссылка: 
Маркович Н.М. Nonparametric estimation of extremal index with smoothing / Book of Abstracts of the 4th Conference of the International Society for Nonparametric Statistics (ISNPS 2018, Salerno, Italy). Salerno: Creative Commons CC BY-NC-ND 4.0 License, 2018. С. 79-80.