The Annals of Statistics

Current status and right-censored data structures when observing a marker at the censoring time

Nicholas P. Jewell and Mark J. Van der Laan

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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.

Article information

Ann. Statist., Volume 31, Number 2 (2003), 512-535.

First available in Project Euclid: 22 April 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation
Secondary: 62F12: Asymptotic properties of estimators

Asymptotically linear estimator asymptotically efficient estimator current status data right-censored data isotonic regression


Van der Laan, Mark J.; Jewell, Nicholas P. Current status and right-censored data structures when observing a marker at the censoring time. Ann. Statist. 31 (2003), no. 2, 512--535. doi:10.1214/aos/1051027879.

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