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Estimating a Distribution Function for Censored Time Series Data

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  • Cai, Zongwu

Abstract

Consider a long term study, where a series of dependent and possibly censored failure times is observed. Suppose that the failure times have a common marginal distribution function, but they exhibit a mode of time series structure such as [alpha]-mixing. The inference on the marginal distribution function is of interest to us. The main results of this article show that, under some regularity conditions, the Kaplan-Meier estimator enjoys uniform consistency with rates, and a stochastic process generated by the Kaplan-Meier estimator converges weakly to a certain Gaussian process with a specified covariance structure. Finally, an estimator of the limiting variance of the Kaplan-Meier estimator is proposed and its consistency is established.

Suggested Citation

  • Cai, Zongwu, 2001. "Estimating a Distribution Function for Censored Time Series Data," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 299-318, August.
    • Handle: RePEc:eee:jmvana:v:78:y:2001:i:2:p:299-318
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    References listed on IDEAS

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    1. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(2), pages 214-252, April.
    2. Koehler, K. J. & Symanowski, J. T., 1995. "Constructing Multivariate Distributions with Specific Marginal Distributions," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 261-282, November.
    3. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    4. Cai, Zongwu, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
    5. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
    6. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
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    Cited by:

    1. Liang, Han-Ying & de Ua-lvarez, Jacobo, 2009. "A Berry-Esseen type bound in kernel density estimation for strong mixing censored samples," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1219-1231, July.
    2. Zhou, Xing-cai & Xu, Ying-zhi & Lin, Jin-guan, 2017. "Wavelet estimation in varying coefficient models for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 179-189.
    3. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.

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