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Strong representation of the presmoothed quantile function estimator for censored data

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  • M. A. Jácome
  • R. Cao

Abstract

We consider lifetime data subject to right random censorship. In this context, this paper deals with the topic of estimating the distribution function of the lifetime and the corresponding quantile function. As it has been shown that the classical Kaplan–Meier estimator of the distribution function can be improved by means of presmoothing ideas, we introduce a quantile function estimator via the presmoothed distribution function estimator studied by Cao et al. [Journal of Nonparametric statistics, Vol. 17 (2005) pp. 31–56.] The main result of this paper is an almost sure representation of this presmoothed estimator. As a consequence, its strong consistency and asymptotic normality are established. The performance of this new quantile estimator is analyzed in a simulation study and applied to a real data example.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:62:y:2008:i:4:p:425-440
    DOI: 10.1111/j.1467-9574.2008.00388.x
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    References listed on IDEAS

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    1. Lio, Y. L. & Padgett, W. J., 1987. "Some convergence results for kernel-type quantile estimators under censoring," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 5-14, January.
    2. Cheng, Philip E. & Lin, Gwo Dong, 1987. "Maximum likelihood estimation of a survival function under the koziol-green proportional hazards model," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 75-80, January.
    3. 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.
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