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Survival function and density estimation for truncated dependent data

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  • Sun, Liuquan
  • Zhou, Xian
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    Abstract

    In some long-term studies, a series of dependent and possibly truncated lifetimes may be observed. Suppose that the lifetimes have a common marginal distribution function. Under some regularity conditions, we provide a strong representation of the product-limit estimator in the form of an average of random variables plus a remainder term. In addition, we also give asymptotic representations for the kernel estimators of the density and the hazard rate. These representations enable us to obtain the asymptotic normality and the uniform consistency of the estimators.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 52 (2001)
    Issue (Month): 1 (March)
    Pages: 47-57

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    Handle: RePEc:eee:stapro:v:52:y:2001:i:1:p:47-57

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    Keywords: [alpha]-mixing; Product-limit estimator Kernel density and hazard rate estimation Strong representation;

    References

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    1. Cai, Zongwu, 1998. "Kernel Density and Hazard Rate Estimation for Censored Dependent Data," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 23-34, October.
    2. Gijbels, I. & Wang, J. L., 1993. "Strong Representations of the Survival Function Estimator for Truncated and Censored Data with Applications," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 210-229, November.
    3. Sun, Liuquan & Zhou, Yong, 1998. "Sequential confidence bands for densities under truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 31-41, September.
    4. Sun, Liuquan, 1997. "Bandwidth choice for hazard rate estimators from left truncated and right censored data," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 101-114, December.
    5. Arcones, Miguel A. & Giné, Evarist, 1995. "On the law of the iterated logarithm for canonical U-statistics and processes," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 217-245, August.
    6. Cai, Zongwu, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
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    Cited by:
    1. Hirose, Hideo, 2007. "The mixed trunsored model with applications to SARS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(6), pages 443-453.
    2. Ghalibaf, M. Bolbolian & Fakoor, V. & Azarnoosh, H.A., 2010. "Strong Gaussian approximations of product-limit and quantile processes for truncated data under strong mixing," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 581-586, April.
    3. Guessoum, Zohra & Ould Saïd, Elias & Sadki, Ourida & Tatachak, Abdelkader, 2012. "A note on the Lynden-Bell estimator under association," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1994-2000.

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