Estimating the probability of a rare event
de Haan, Laurens ; Sinha, Ashoke Kumar
Ann. Statist., Tome 27 (1999) no. 4, p. 732-759 / Harvested from Project Euclid
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Let $(X_{1},Y_{1}), (X_{2},Y_{2}),\dots,(X_{n},Y_{n})$ be a random sample from a bivariate distribution function $F$ which is in the domain of attraction of a bivariate extreme value distribution function $G$. A subset $C$ of $\mathbb{R}^{2}$ is given, which contains none of the observations. We shall give an asymptotic confidence interval for $\Pr((X_{i},Y_{i}) \in C)$ under certain conditions.
Publié le : 1999-04-14
Classification:  Failure region,  failure chance,  empirical process,  estimation,  functional central limit theorem,  multivariate extremes,  Vapnik-Cervonenkis class.,  62H10,  62P99 
@article{1018031214,
     author = {de Haan, Laurens and Sinha, Ashoke Kumar},
     title = {Estimating the probability of a rare event},
     journal = {Ann. Statist.},
     volume = {27},
     number = {4},
     year = {1999},
     pages = { 732-759},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1018031214}
}

de Haan, Laurens; Sinha, Ashoke Kumar. Estimating the probability of a rare event. Ann. Statist., Tome 27 (1999) no. 4, pp.  732-759. http://gdmltest.u-ga.fr/item/1018031214/