Electronic Journal of Statistics

Cumulative distribution function estimation under interval censoring case 1

Elodie Brunel and Fabienne Comte

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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.

Article information

Electron. J. Statist., Volume 3 (2009), 1-24.

First available in Project Euclid: 28 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties

Adaptive estimation Current status data Minimax rate Interval censoring Nonparametric estimator Penalized contrast


Brunel, Elodie; Comte, Fabienne. Cumulative distribution function estimation under interval censoring case 1. Electron. J. Statist. 3 (2009), 1--24. doi:10.1214/08-EJS209. https://projecteuclid.org/euclid.ejs/1233176788

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