Some convergence results for kernel-type quantile estimators under censoring
type: Item
instance of: scholarly article
title: Some convergence results for kernel-type quantile estimators under censoring
zbMATH Open document ID: 0608.62049
DOI: 10.1016/0167-7152(87)90018-6
author: W. J. Padgett
author: Yuhlong Lio
published in: Statistics \& Probability Letters
publication date: 1987-01-01T00:00:00Z
review text: In continuation of the investigations of the authors and \textit{K. F. Yu} reviewed above, Zbl 0608.62048, the authors use some strong results on the product-limit estimator and its quantile function, provided by various authors to derive the following: i) Asymptotic normality of \(\sqrt{n}(Q_ n(p)-F^{-1}(p))\), as above, but for arbitrary null-sequence \(h_ n.\) ii) Rates of convergence of \(Q_ n(p)-Q_ n^*(p)\) w.r. to \(L_ 1\) and \(L_ 2\) norms. iii) \(E(Q_ n(p)-F^{-1}(p))^ 2=O(h_ n+h_ n^{1/2}n^{- 5/4}+((\log n)/n)^{3/4})\), as \(n\to \infty\), provided some assumptions on F,K and \(h_ n\) are satisfied.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 3984337
zbMATH Keywords: random-right-censorship model
zbMATH Keywords: kernel smoothed quantile function
zbMATH Keywords: bounds for mean-square-error
zbMATH Keywords: product-limit estimator
zbMATH Keywords: Asymptotic normality
zbMATH Keywords: Rates of convergence
reviewed by: Ulrich Stadtmüller
MaRDI profile type: Publication
full work available at URL: 0167-7152(87)90018-6
OpenAlex ID: W1970283837
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description: scientific article; zbMATH DE number 3984337