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Kernel Density and Hazard Rate Estimation for Censored Dependent Data

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  • Cai, Zongwu

Abstract

In some long term studies, a series of dependent and possibly censored failure times may be observed. Suppose that the failure times have a common marginal distribution function having a density, and the nonparametric estimation of density and hazard rate under random censorship is of our interest. In this paper, we establish the asymptotic normality and the uniform consistency (with rates) of the kernel estimators for density and hazard function under a censored dependent model. A numerical study elucidates the behavior of the estimators for moderately large sample sizes.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:67:y:1998:i:1:p:23-34
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    References listed on IDEAS

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    1. Diehl, Sabine & Stute, Winfried, 1988. "Kernel density and hazard function estimation in the presence of censoring," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 299-310, May.
    2. 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. E.I., Abdul Sathar & K.V., Viswakala, 2019. "Non-parametric estimation of Kullback–Leibler discrimination information based on censored data," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    2. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V. K., 2006. "Density and hazard rate estimation for censored and a-mixing data using gamma kernels," LIDAM Discussion Papers CORE 2006118, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Taoufik Bouezmarni & Jeroen Rombouts, 2008. "Density and hazard rate estimation for censored and α-mixing data using gamma kernels," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 627-643.
    4. Diallo, Amadou Oury Korbe & Louani, Djamal, 2013. "Moderate and large deviation principles for the hazard rate function kernel estimator under censoring," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 735-743.
    5. Sun, Liuquan & Zhou, Xian, 2001. "Survival function and density estimation for truncated dependent data," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 47-57, March.
    6. R. Maya & E. Abdul-Sathar & G. Rajesh & K. Muraleedharan Nair, 2014. "Estimation of the Renyi’s residual entropy of order $$\alpha $$ with dependent data," Statistical Papers, Springer, vol. 55(3), pages 585-602, August.
    7. Maya, R. & Abdul-Sathar, E.I. & Rajesh, G., 2014. "Non-parametric estimation of the generalized past entropy function with censored dependent data," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 129-135.
    8. Liang Han-Ying & Mammitzsch Volker & Steinebach Josef, 2005. "Nonlinear wavelet density and hazard rate estimation for censored data under dependent observations," Statistics & Risk Modeling, De Gruyter, vol. 23(3/2005), pages 161-180, March.
    9. Fakoor, V., 2010. "Strong uniform consistency of kernel density estimators under a censored dependent model," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 318-323, March.

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