Electronic Journal of Statistics

Cumulative distribution function estimation under interval censoring case 1

Elodie Brunel and Fabienne Comte

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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.

Article information

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

Dates
First available in Project Euclid: 28 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1233176788

Digital Object Identifier
doi:10.1214/08-EJS209

Mathematical Reviews number (MathSciNet)
MR2471584

Zentralblatt MATH identifier
1326.62075

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

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

Citation

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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