In this paper we consider the TJW product-limit estimator F 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 n (x) is derived with an improved error bound under some weaker assumption
Strong Representations of the Survival Function Estimator for Truncated and Censored Data with Applications
β Scribed by I. Gijbels; J.L. Wang
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 514 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0047-259X
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β¦ Synopsis
A strong i.i.d. representation is obtained for the product-limit estimator of the survival function based on left truncated and right censored data. This extends the result of Chao and Lo (1988, Ann. Statist. 16, 661-668) for truncated data. An improved rate of the approximation is also obtained on compact sets. Applications include density and hazard rate estimation. The advantage of the improved rate of the approximation is illustrated via kernel density estimation. 1993 Academic Press, Inc.
π SIMILAR VOLUMES
Randomly left or right truncated observations occur when one is concerned with estimation of the distribution of time between two events and when one only observes the time if one of the two events falls in a fixed time-window, so that longer survivial times have higher probability to be part of the