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Smoothed estimator of quantile residual lifetime for right censored data

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Abstract

It is of great interest to estimate quantile residual lifetime in medical science and many other fields. In survival analysis, Kaplan-Meier (K-M) estimator has been widely used to estimate the survival distribution. However, it is well-known that the K-M estimator is not continuous, thus it can not always be used to calculate quantile residual lifetime. In this paper, the authors propose a kernel smoothing method to give an estimator of quantile residual lifetime. By using modern empirical process techniques, the consistency and the asymptotic normality of the proposed estimator are provided neatly. The authors also present the empirical small sample performances of the estimator. Deficiency is introduced to compare the performance of the proposed estimator with the naive unsmoothed estimator of the quantile residaul lifetime. Further simulation studies indicate that the proposed estimator performs very well.

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Authors and Affiliations

  1. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, 200433, China

    Li Zhang & Yong Zhou

  2. Academy of Mathematics and System Sciences, Chinese Academy of Science, Beijing, 100190, China

    Peng Liu & Yong Zhou

Authors
  1. Li Zhang
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  2. Peng Liu
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  3. Yong Zhou
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Corresponding author

Correspondence to Li Zhang.

Additional information

ZHOU’s work was supported by the National Natural Science Foundation of China under Grant No. 71271128, the State Key Program of National Natural Science Foundation of China under Grant No. 71331006, NCMIS, Key Laboratory of RCSDS, CAS and IRTSHUFE, PCSIRT (IRT13077). ZHANG’s work was supported by Graduate Innovation Fund of Shanghai University of Finance and Economics under Grant No. CXJJ-2011-429.

This paper was recommended for publication by Editor SUN Liuquan.

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Zhang, L., Liu, P. & Zhou, Y. Smoothed estimator of quantile residual lifetime for right censored data. J Syst Sci Complex 28, 1374–1388 (2015). https://doi.org/10.1007/s11424-015-3067-7

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  • DOI: https://doi.org/10.1007/s11424-015-3067-7

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