Bahadur Representation of the Kernel Quantile Estimator under Random Censorship

X. J. Xiang

Journal of Multivariate Analysis, 1995, vol. 54, issue 2, 193-209

Abstract: 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.

Date: 1995
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