A histogram estimator of the hazard rate with censored data
type: Item
instance of: scholarly article
title: A histogram estimator of the hazard rate with censored data
zbMATH Open document ID: 0612.62059
author: Regina Y. Liu
author: John van Ryzin
published in: The Annals of Statistics
publication date: 1985-01-01T00:00:00Z
review text: Let \(X_ 1,...,X_ n\) denote lifetimes for the n subjects under study, and \(C_ 1,...,C_ n\) be the corresponding censoring times. The observed random variables are the \(Z_ i\) and \(\delta_ i\) where \(Z_ i=\min (X_ i,C_ i)\) and \(\delta_ i=I(X_ i\leq C_ i)\). The authors assume throughout the paper that (i) \(X_ 1,...,X_ n\) are nonnegative and i.i.d. with common d.f. F and continuous density f, (ii) \(C_ 1,...,C_ n\) are nonnegative and i.i.d. with common continuous d.f. G and continuous density g, and (iii) lifetimes and censoring times are independent. The problem considered here is estimation of the hazard rate function given by \[ \lambda (x)=f(x)/(1-F(x)),\quad F(x)<1. \] The proposed estimator is based on random spacings of the order statistics of uncensored observations. The authors establish pointwise large sample properties of the estimator including strong consistency on a bounded interval, and two asymptotic results.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62P10
zbMATH DE Number: 3990636
zbMATH Keywords: histogram type estimator
zbMATH Keywords: randomly right-censored
zbMATH Keywords: strong uniform consistency
zbMATH Keywords: best rate of convergence
zbMATH Keywords: asymptotic normality
zbMATH Keywords: lifetimes
zbMATH Keywords: censoring times
zbMATH Keywords: hazard rate function
zbMATH Keywords: random spacings
zbMATH Keywords: order statistics
zbMATH Keywords: pointwise large sample properties
zbMATH Keywords: strong consistency
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349541
OpenAlex ID: W2047458644
DOI: 10.1214/AOS/1176349541
description: scientific article; zbMATH DE number 3990636