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| HAL: hal-00557307, version 1 |
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| Available versions: | v1 (2011-01-19) | v2 (2011-11-28) |
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| Inhomogeneous and Anisotropic Conditional Density Estimation from Dependent Data |
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| Nathalie Akakpo 1Claire Lacour 2 |
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| (2011) |
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| The problem of estimating a conditional density is considered. Given a collection of partitions, we propose a procedure that selects from the data the best partition among that collection and then provides the best piecewise polynomial estimator built on that partition. The observations are not supposed to be independent but only $\beta$-mixing; in particular, our study includes the estimation of the transition density of a Markov chain. For a well-chosen collection of possibly irregular partitions, we obtain oracle-type inequalities and adaptivity results in the minimax sense over a wide range of possibly anisotropic and inhomogeneous Besov classes. We end with a short simulation study. |
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| 1: | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot |
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| 2: | Laboratoire de Mathématiques d'Orsay (LM-Orsay) |
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CNRS : UMR8628 – Université Paris XI - Paris Sud |
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| Subject | : | Mathematics/Statistics Statistics/Statistics Theory |
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| hal-00557307, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00557307 | |
| oai:hal.archives-ouvertes.fr:hal-00557307 | |
| From: Claire Lacour | |
| Submitted on: Tuesday, 18 January 2011 22:49:56 | |
| Updated on: Wednesday, 19 January 2011 08:34:06 | |
