Functional nonparametric estimation of conditional extreme quantiles

TL;DR

This paper introduces nonparametric methods for estimating extreme quantiles in heavy-tailed distributions with functional covariates, analyzing their asymptotic properties and finite sample performance.

Contribution

It proposes novel nonparametric estimators for functional extreme quantiles and studies their theoretical and finite sample behaviors.

Findings

Asymptotic distributions of the estimators are derived.

Finite sample performance is evaluated through simulations.

Estimators perform well near the boundary of the data range.

Abstract

We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such "extreme" quantiles can be located in the range of the data or near and even beyond the boundary of the sample, depending on the convergence rate of their order to one. Nonparametric estimators of these functional extreme quantiles are introduced, their asymptotic distributions are established and their finite sample behavior is investigated.