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Bahadur Representation of the Kernel Quantile Estimator under Random Censorship

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  • Xiang, X. J.

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.

Suggested Citation

  • Xiang, X. J., 1995. "Bahadur Representation of the Kernel Quantile Estimator under Random Censorship," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 193-209, August.
    • Handle: RePEc:eee:jmvana:v:54:y:1995:i:2:p:193-209
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    Cited by:

    1. Ajami, M. & Fakoor, V. & Jomhoori, S., 2011. "The Bahadur representation for kernel-type estimator of the quantile function under strong mixing and censored data," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1306-1310, August.
    2. M. A. Jácome & R. Cao, 2008. "Strong representation of the presmoothed quantile function estimator for censored data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(4), pages 425-440, November.

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