Current status censoring (CSC) implies that there is no direct access to the lifetime of an event of interest. Instead it is known if the event already occurred or not at a random monitoring time. CSC is a simple sampling procedure and in many cases the only possibility to assess the lifetime of interest. At the same time, the absence of a direct measurement of a lifetime of interest makes the problem of nonparametric distribution estimation ill-posed. A simple, adaptive and sharp minimax estimator of the density and cumulative distribution function is proposed. The simplicity of estimator also allows us to relax assumptions. Practical examples illustrate CSC problem and the proposed estimator.
The author would like to thank two referees, an Associate Editor and the Editor for constructive comments that improved the quality of this paper. The research was supported by NSF Grant DMS-1915845 and Grants from BIFAR and CAS.
"Efficient nonparametric estimation of distribution for current status censoring." Electron. J. Statist. 16 (1) 998 - 1057, 2022. https://doi.org/10.1214/22-EJS1980