# Kernel Density and Hazard Rate Estimation for Censored Dependent Data

Listed:
• 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.

## Suggested Citation

• 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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File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(98)91752-3

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## References listed on IDEAS

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1. Cai, Zongwu, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
2. 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.
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## Citations

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Cited by:

1. 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.
2. 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.
3. 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.
4. 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.
5. Taoufik Bouezmarni & Jeroen V.K. Rombouts, 2006. "Density and Hazard Rate Estimation for Censored and ?-mixing Data Using Gamma Kernels," Cahiers de recherche 06-16, HEC Montréal, Institut d'économie appliquée.
6. 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.
7. 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.

### Keywords

[alpha]-mixing asymptotic normality censoring convergence rate density function hazard rate kernel estimation;

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