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

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 22 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1051027879

Digital Object Identifier
doi:10.1214/aos/1051027879

Mathematical Reviews number (MathSciNet)
MR1983540

Zentralblatt MATH identifier
1039.62095

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1051027879


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  • BERKELEY, CALIFORNIA 94720 E-MAIL: laan@stat.berkeley.edu