## Current status and right-censored data structures when observing a marker at the censoring time.(English)Zbl 1039.62095

Summary: We study nonparametric estimation with two types of data structures. In the first data structure $$n$$ i.i.d. copies of $$(C N(C))$$ are observed, where $$N$$ is a finite state counting process jumping at time-variables of interest and $$C$$ a random monitoring time. In the second data structure $$n$$ i.i.d. copies of $$(C\wedge T,I(T\leq C)$$, $$N(C \wedge T))$$ are observed, where $$N$$ is a counting process with a final jump at time $$T$$ (e.g., death). This data structure includes observing right-censored data on $$T$$ and a marker variable at the censoring time.
In these data structures, easy to compute estimators, namely (weighted)-pool-adjacent-violator estimators for the marginal distributions of the unobservable time variables, and the Kaplan-Meier estimator for the time $$T$$ till the final observable event, are available. These estimators ignore seemingly important information in the data. In this paper we prove that at many continuous data generating distributions the ad hoc estimators yield asymptotically efficient estimators of $$\sqrt n$$-estimable parameters.

### MSC:

 62N02 Estimation in survival analysis and censored data 62N01 Censored data models 62G05 Nonparametric estimation 62F12 Asymptotic properties of parametric estimators 62G07 Density estimation
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### References:

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