Geodesic
Estimating the conditional density by histogram type estimators and model selection
Sart, Mathieu1
1 Univ Lyon, UJM-Saint-Etienne, CNRS, Institut Camille Jordan UMR 5208, 42023, Saint-Etienne, France.
ESAIM: Probability and Statistics, Tome 21 (2017), pp. 34-55

Voir la notice de l'article provenant de la source Numdam

We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By using a deterministic Hellinger distance as loss, we prove that the selected function satisfies a non-asymptotic oracle type inequality under minimal assumptions on the statistical setting. We derive an adaptive piecewise constant estimator on a random partition that achieves the expected rate of convergence over (possibly inhomogeneous and anisotropic) Besov spaces of small regularity. Moreover, we show that this oracle inequality may lead to a general model selection theorem under very mild assumptions on the statistical setting. This theorem guarantees the existence of estimators possessing nice statistical properties under various assumptions on the conditional density (such as smoothness or structural ones).

Reçu le :
Accepté le :
DOI : 10.1051/ps/2016026
Classification : 62G05, 62G07
Keywords: Adaptive estimation, conditional density, histogram, model selection, robust tests

Sart, Mathieu 1

1 Univ Lyon, UJM-Saint-Etienne, CNRS, Institut Camille Jordan UMR 5208, 42023, Saint-Etienne, France. 
@article{PS_2017__21__34_0,
     author = {Sart, Mathieu},
     title = {Estimating the conditional density by histogram type estimators and model selection},
     journal = {ESAIM: Probability and Statistics},
     pages = {34--55},
     publisher = {EDP-Sciences},
     volume = {21},
     year = {2017},
     doi = {10.1051/ps/2016026},
     mrnumber = {3630602},
     zbl = {1453.62447},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2016026/}
}
TY  - JOUR
AU  - Sart, Mathieu
TI  - Estimating the conditional density by histogram type estimators and model selection
JO  - ESAIM: Probability and Statistics
PY  - 2017
SP  - 34
EP  - 55
VL  - 21
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ps/2016026/
DO  - 10.1051/ps/2016026
LA  - en
ID  - PS_2017__21__34_0
ER  - 
%0 Journal Article
%A Sart, Mathieu
%T Estimating the conditional density by histogram type estimators and model selection
%J ESAIM: Probability and Statistics
%D 2017
%P 34-55
%V 21
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ps/2016026/
%R 10.1051/ps/2016026
%G en
%F PS_2017__21__34_0
Sart, Mathieu. Estimating the conditional density by histogram type estimators and model selection. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 34-55. doi: 10.1051/ps/2016026

Cité par Sources :