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university of Provence - Aix-Marseille I |  |
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university of Provence - Aix-Marseille I | |
| HAL: hal-00715260, version 1 |
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| Available versions: | v1 (2012-07-07) | v2 (2013-04-05) | v3 (2013-05-08) |
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| Estimation of a cumulative distribution function under interval censoring ''case 1'' via warped wavelets |
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| Christophe Chesneau 1Thomas Willer 2 |
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| (2012-07-06) |
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| 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 $\mathbb{L}_2$ 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. |
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| 1: | Laboratoire de Mathématiques Nicolas Oresme (LMNO) |
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CNRS : UMR6139 – Université de Caen Basse-Normandie |
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| 2: | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| Subject | : | Mathematics/Statistics Statistics/Statistics Theory |
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| Adaptive estimation – Strongly mixing – Interval censoring – Warped wavelets – Hard thresholding. |
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| hal-00715260, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00715260 | |
| oai:hal.archives-ouvertes.fr:hal-00715260 | |
| From: Christophe Chesneau | |
| Submitted on: Friday, 6 July 2012 15:39:37 | |
| Updated on: Saturday, 7 July 2012 08:53:11 | |
