A general estimator for the right endpoint with an application to supercentenarian women's records

摘要

We extend the setting of the right endpoint estimator introduced in Fraga Alves and Neves (Statist. Sinica 24, 1811-1835, 2014) to the broader class of light-tailed distributions with finite endpoint, belonging to some domain of attraction induced by the extreme value theorem. This stretch enables a general estimator for the finite endpoint, which does not require estimation of the (supposedly non-positive) extreme value index. A new testing procedure for selecting max-domains of attraction also arises in connection with the asymptotic properties of the general endpoint estimator. The simulation study conveys that the general endpoint estimator is a valuable complement to the most usual endpoint estimators, particularly when the true extreme value index stays above -1/2, embracing the most common cases in practical applications. An illustration is provided via an extreme value analysis of supercentenarian women data.