Cumulative distribution function estimation under interval censoring case 1

Details Cumulative distribution function estimation under interval censoring case 1 Cumulative distribution function estimation under interval censoring case 1

2008-03-18

arxiv.org/abs/0803.2586v2

Electronic Journal of Statistics 2009, Vol. 3, 1-24

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-EJS209 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/08-EJS209

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.

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