Electronic Journal of Statistics

Inhomogeneous and anisotropic conditional density estimation from dependent data

Nathalie Akakpo and Claire Lacour

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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 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.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 1618-1653.

Dates
First available in Project Euclid: 7 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1323267565

Digital Object Identifier
doi:10.1214/11-EJS653

Mathematical Reviews number (MathSciNet)
MR2870146

Zentralblatt MATH identifier
1271.62060

Subjects
Primary: 62G05: Estimation 62H12: Estimation 62M05: Markov processes: estimation 62M09: Non-Markovian processes: estimation

Keywords
Conditional density model selection anisotropy dependent data adaptive estimation

Citation

Akakpo, Nathalie; Lacour, Claire. Inhomogeneous and anisotropic conditional density estimation from dependent data. Electron. J. Statist. 5 (2011), 1618--1653. doi:10.1214/11-EJS653. https://projecteuclid.org/euclid.ejs/1323267565


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