# Inhomogeneous and Anisotropic Conditional Density Estimation from Dependent Data

Abstract : 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.
Type de document :
Article dans une revue
Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2011, 5, pp.1618-1653. <10.1214/11-EJS653>
Domaine :

https://hal.archives-ouvertes.fr/hal-00557307
Contributeur : Claire Lacour <>
Soumis le : lundi 28 novembre 2011 - 15:42:30
Dernière modification le : lundi 29 mai 2017 - 14:22:12
Document(s) archivé(s) le : mercredi 29 février 2012 - 02:26:59

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RevdenscondinhomogeneEJS.pdf
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### Citation

Nathalie Akakpo, Claire Lacour. Inhomogeneous and Anisotropic Conditional Density Estimation from Dependent Data. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2011, 5, pp.1618-1653. <10.1214/11-EJS653>. <hal-00557307v2>

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