Bahadur Representation of the Kernel Quantile Estimator under Random Censorship

✍ Scribed by X.J. Xiang

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 439 KB
• Volume: 54
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1995.1052

✦ Synopsis

In this paper, a representation due to Major and Rejtö for the Kaplan-Meier estimator is applied to establish a Bahadur representation for the kernel quantile estimator under random censorship. Comparing it with the product-limit quantile estimator, the convergence rate of the remainder term is substantially improved when (F(x)) is sufficiently smooth near the true quantile (\xi_{p}). As a consequence, a law of the iterated logarithm is also obtained. 1995 Academic Press, Inc.