A strong representation of the product-limit estimator for left truncated and right censored data

	A strong representation of the product-limit estimator for left truncated and right censored data
	Zhou, Y ; Yip, PSF
刊名	JOURNAL OF MULTIVARIATE ANALYSIS
	1999-05-01
卷号	69 期号:2 页码:261-280
关键词	truncated data censored data product-limit estimator almost sure representation
ISSN号	0047-259X
英文摘要	In this paper we consider the TJW product-limit estimator (F) over cap(n)(x) of an unknown distribution function F when the data are subject to random left truncation and right censorship. An almost sure representation of PL-estimator (F) over cap(n)(x) is derived with an improved error bound under some weaker assumptions. We obtain the strong approximation of (F) over cap(n)(x) - F(x) by Gaussian processes and the functional law of the iterated logarithm is proved for maximal derivation of the product-limit estimator to F. A sharp rate of convergence theorem concerning the smoothed TJW product-limit estimator is obtained. Asymptotic properties of kernel estimators of density function based on TJW product-limit estimator is given. (C) 1999 Academic Press. AMS 1991 subject classifications: 62G05, 60F17, 62E20, 62G20.
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC
WOS记录号	WOS:000080242200007
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/14852]
专题	中国科学院数学与系统科学研究院
通讯作者	Zhou, Y
作者单位	1.Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China 2.Univ Hong Kong, Dept Stat, Hong Kong, Hong Kong
推荐引用方式 GB/T 7714	Zhou, Y,Yip, PSF. A strong representation of the product-limit estimator for left truncated and right censored data[J]. JOURNAL OF MULTIVARIATE ANALYSIS,1999,69(2):261-280.
APA	Zhou, Y,&Yip, PSF.(1999).A strong representation of the product-limit estimator for left truncated and right censored data.JOURNAL OF MULTIVARIATE ANALYSIS,69(2),261-280.
MLA	Zhou, Y,et al."A strong representation of the product-limit estimator for left truncated and right censored data".JOURNAL OF MULTIVARIATE ANALYSIS 69.2(1999):261-280.