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

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  • Christophe Chesneau
  • Thomas Willer

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.

Suggested Citation

  • Christophe Chesneau & Thomas Willer, 2015. "Estimation of a Cumulative Distribution Function Under Interval Censoring “case 1” Via Warped Wavelets," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(17), pages 3680-3702, September.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:17:p:3680-3702
    DOI: 10.1080/03610926.2013.851231
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