Functional kernel estimators of conditional extreme quantiles

TL;DR

This paper develops kernel-based methods for estimating extreme conditional quantiles that approach the maximum as sample size grows, providing asymptotic properties and practical estimators for tail behavior.

Contribution

It introduces new kernel estimators for extreme conditional quantiles and tail indices, with conditions ensuring their asymptotic Gaussian distribution.

Findings

Asymptotic Gaussian distribution of estimators established

New Weissman-type estimator for extreme quantiles proposed

Kernel estimators for tail-index of conditional distributions derived

Abstract

We address the estimation of "extreme" conditional quantiles i.e. when their order converges to one as the sample size increases. Conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian distributed kernel estimators. A Weissman-type estimator and kernel estimators of the conditional tail-index are derived, permitting to estimate extreme conditional quantiles of arbitrary order.