Tail estimates motivated by extreme value theory (Q760731)

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.