Tail estimates motivated by extreme value theory. (English) Zbl 0555.62035

This paper deals with the problem of estimating the upper tail of a distribution function. The proposed estimator is based on the upper m order statistics from a random sample of size n (m\(\to \infty\), m/n\(\to 0\) as \(n\to \infty)\) and is shown to be consistent for a wide class of distribution functions. Since the empirical mean residual life of the log transformed data and the sample 1-m/n quantile play a key role in the estimator, their joint asymptotic behavior is studied, and rates of convergence of the estimator to the tail are obtained.
Reviewer: J.Melamed


62G05 Nonparametric estimation
62G30 Order statistics; empirical distribution functions
62F12 Asymptotic properties of parametric estimators
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