  The Pickands estimator for the extreme value index is beneficial due to its
universal consistency, location, and scale invariance, which sets it apart from
other types of estimators. However, similar to many extreme value index
estimators, it is marked by poor asymptotic efficiency. Chen (2021) introduces
a Conditional Value-at-Risk (CVaR)-based Pickands estimator, establishes its
consistency, and demonstrates through simulations that this estimator
significantly reduces mean squared error while preserving its location and
scale invariance. The initial focus of this paper is on demonstrating the weak
convergence of the empirical CVaR in functional space. Subsequently, based on
the established weak convergence, the paper presents the asymptotic normality
of the CVaR-based Pickands estimator. It further supports these theoretical
findings with empirical evidence obtained through simulation studies.
