Some large sample properties of an estimator of the hazard function from randomly censored data
type: Item
instance of: scholarly article
title: Some large sample properties of an estimator of the hazard function from randomly censored data
zbMATH Open document ID: 0821.62021
published in: Chinese Science Bulletin
publication date: 1995-08-09T00:00:00Z
review text: In many lifetime studies, some of the subjects under study are censored on the right by a prior censoring time. We observe only the censored data. It is important to estimate the life characteristics of the subjects. Let \(T_ 1\), \(T_ 2, \dots, T_ n\) be independent and identically distributed nonnegative random variables with common continuous distribution function \(F\) and continuous probability density function \(f\). In the model of right random censoring, associated with each \(T_ i\) there is an independent nonnegative censoring time \(C_ i\) and \(C_ 1\), \(C_ 2, \dots, C_ n\) are assumed to be iid random variables with continuous distribution function \(G\). In this model we can observe only the pairs \((Z_ i, \delta_ i)\), where \(Z_ i = \min (T_ i, C_ i)\), \(\delta_ i = I[T_ i \leq C_ i]\), \(i = 1,2, \dots, n\), and \(I[\cdot]\) is the indicator function of a certain event. Clearly \(Z_ 1\), \(Z_ 2, \dots, Z_ n\) are iid with continuous distribution function \(H = 1 - (1 - F) (1 - G)\). The problem considered is to estimate the hazard function \(\lambda (t) = f(t)/(1 - F(t))\) by using the above censoring data observed and investigate the large sample properties.
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62N05
Mathematics Subject Classification ID: 62P10
zbMATH DE Number: 783507
zbMATH Keywords: lifetime studies
zbMATH Keywords: random censoring
zbMATH Keywords: hazard function
author: Qihua Wang
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 783507