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A strong representation of the product-limit estimator for left truncated and right censored data
Zhou, Y; Yip, PSF
1999-05-01
Source PublicationJOURNAL OF MULTIVARIATE ANALYSIS
ISSN0047-259X
Volume69Issue:2Pages:261-280
AbstractIn 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.
Keywordtruncated data censored data product-limit estimator almost sure representation
Language英语
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000080242200007
PublisherACADEMIC PRESS INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/14853
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZhou, Y
Affiliation1.Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China
2.Univ Hong Kong, Dept Stat, Hong Kong, Hong Kong
Recommended Citation
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.
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