Open Access
2011 Inhomogeneous and anisotropic conditional density estimation from dependent data
Nathalie Akakpo, Claire Lacour
Electron. J. Statist. 5: 1618-1653 (2011). DOI: 10.1214/11-EJS653


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 β-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.


Download Citation

Nathalie Akakpo. Claire Lacour. "Inhomogeneous and anisotropic conditional density estimation from dependent data." Electron. J. Statist. 5 1618 - 1653, 2011.


Published: 2011
First available in Project Euclid: 7 December 2011

zbMATH: 1271.62060
MathSciNet: MR2870146
Digital Object Identifier: 10.1214/11-EJS653

Primary: 62G05 , 62H12 , 62M05 , 62M09

Keywords: adaptive estimation , Anisotropy , Conditional density , dependent data , Model selection

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

Back to Top