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Estimating a distribution function for censored time series data. (English) Zbl 1057.62068

Summary: 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.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. (statistics) 62G07 Density estimation 60F05 Central limit and other weak theorems 62G05 Nonparametric estimation 62M09 Non-Markovian processes: estimation