TITLE:
Functional Kernel Estimation of the Conditional Extreme Quantile under Random Right Censoring
AUTHORS:
Justin Ushize Rutikanga, Aliou Diop
KEYWORDS:
Kernel Estimator, Functional Data, Censored Data, Conditional Extreme Quantile, Heavy-Tailed Distributions
JOURNAL NAME:
Open Journal of Statistics,
Vol.11 No.1,
February
7,
2021
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.