A Strong Representation of the Product-Limit Estimator for Left Truncated and Right Censored Data

✍ Scribed by Yong Zhou; Paul S.F. Yip

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 162 KB
• Volume: 69
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1998.1806

✦ Synopsis

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 assumptions. We obtain the strong approximation of F 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 productlimit estimator is obtained. Asymptotic properties of kernel estimators of density function based on TJW product-limit estimator is given.