Cumulative distribution function estimation under interval censoring case 1

TL;DR

This paper investigates projection-based methods for estimating the cumulative distribution function under interval censoring case 1, focusing on adaptive estimators that achieve optimal rates with some restrictions, supported by simulations.

Contribution

It introduces two adaptive estimators for interval censored data, demonstrating their optimal convergence rates and comparing their performance through simulations.

Findings

Both estimators achieve optimal convergence rates.

The quotient estimator has some restrictions.

Simulation results illustrate estimator performance.

Abstract

We consider projection methods for the estimation of the cumulative distribution function under interval censoring, case 1. Such censored data also known as current status data, arise when the only information available on the variable of interest is whether it is greater or less than an observed random time. Two types of adaptive estimators are investigated. The first one is a two-step estimator built as a quotient estimator. The second estimator results from a mean square regression contrast. Both estimators are proved to achieve automatically the standard optimal rate associated with the unknown regularity of the function, but with some restriction for the quotient estimator. Simulation experiments are presented to illustrate and compare the methods.