title: An Investigation of Quantile Function Estimators Relative to Quantile Confidence Interval Coverage.
abstract: In this article, we investigate the limitations of traditional quantile function estimators and introduce a new class of quantile function estimators, namely, the semi-parametric tail-extrapolated quantile estimators, which has excellent performance for estimating the extreme tails with finite sample sizes. The smoothed bootstrap and direct density estimation via the characteristic function methods are developed for the estimation of confidence intervals. Through a comprehensive simulation study to compare the confidence interval estimations of various quantile estimators, we discuss the preferred quantile estimator in conjunction with the confidence interval estimation method to use under different circumstances. Data examples are given to illustrate the superiority of the semi-parametric tail-extrapolated quantile estimators. The new class of quantile estimators is obtained by slight modification of traditional quantile estimators, and therefore, should be specifically appealing to researchers in estimating the extreme tails.
authors.affiliation: Department of Biostatistics, State University of New York at Buffalo, Buffalo, New York, USA.
authors.forename: Lai
authors.initials: L
authors.lastname: Wei
authors.affiliation: Department of Public Health and Preventive Medicine, State University of New York Upstate Medical University, Syracuse, New York, USA.
authors.forename: Dongliang
authors.initials: D
authors.lastname: Wang
authors.affiliation: Department of Biostatistics, State University of New York at Buffalo, Buffalo, New York, USA.
authors.forename: Alan D
authors.initials: AD
authors.lastname: Hutson
keywords: Characteristic function; Direct density estimation; Inversion theorem; Smoothed bootstrap; Tail extrapolation