Estimation of a Cumulative Distribution Function Under Interval Censoring “case 1” Via Warped Wavelets

Christophe Chesneau and Thomas Willer

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 17, 3680-3702

Abstract: The estimation of an unknown cumulative distribution function in the interval censoring “case 1” model from dependent sequences is considered. We construct a new adaptive estimator based on a warped wavelet basis and a hard thresholding rule. Under mild assumptions on the parameters of the model, considering the L2$\mathbb {L}_2$ risk and the weighted Besov balls, we prove that the estimator attains a sharp rate of convergence. We also investigate its practical performances thanks to simulation experiments.

Date: 2015
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DOI: 10.1080/03610926.2013.851231

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