Abstract
The study of estimation of conditional extreme quantile in incomplete data frameworks is of growing interest. Specially, the estimation of the extreme value index in a censorship framework has been the purpose of many investigations when finite dimension covariate information has been considered. In this paper, the estimation of the conditional extreme quantile of a heavy-tailed distribution is discussed when some functional random covariate (i.e. valued in some infinite-dimensional space) information is available and the scalar response variable is right-censored. A Weissman-type estimator of conditional extreme quantiles is proposed and its asymptotic normality is established under mild assumptions. A simulation study is conducted to assess the finite-sample behavior of the proposed estimator and a comparison with two simple estimations strategies is provided.
Highlights
Estimation of extreme quantile is one of the most important keys in many studies of rare events that happen occasionally but have a big impact on the behaviors of distribution of these rare events
The useful material for modeling those types of extreme events are provided by Extreme Value Theory (EVT), such as estimation of tailed index and associated extreme quantile
We focus on the problem of estimating a conditional extreme-quantile of a heavy-tailed distribution when some functional covariate information X ∈ E is available, where
Summary
Estimation of extreme quantile is one of the most important keys in many studies of rare events that happen occasionally but have a big impact on the behaviors of distribution of these rare events. When some covariate information X is available and the distribution of Y depends on X, the problem is to estimate the conditional extreme-value index and conditional extreme quantiles. We focus on the problem of estimating a conditional extreme-quantile of a heavy-tailed distribution when some functional covariate information X ∈ E is available, where. Daouia et al [5] introduced the kernel-type estimation of the extreme conditional quantile q (αn | x) from heavy-tailed distribution which belongs to Fréchet maximum domain of attraction, while [6] proposed new estimation procedure for estimating the conditional survival function F ( y | x) := 1− F ( y | x) by considering different double kernel estimator.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
