We propose a general partition-based strategy to estimate conditional density with candidate densities that are piecewise constant with respect to the covariate. Capitalizing on a general penalized maximum likelihood model selection result, we prove, on two specific examples, that the penalty of each model can be chosen roughly proportional to its dimension. We first study a classical strategy in which the densities are chosen piecewise conditional according to the variable. We then consider Gaussian mixture models with mixing proportion that vary according to the covariate but with common mixture components. This model proves to be interesting for an unsupervised segmentation application that was our original motivation for this work.
Mots-clés : conditional density estimation, partition, penalized likelihood, piecewise polynomial density, gaussian mixture model
@article{PS_2013__17__672_0,
author = {Cohen, S. X. and Le Pennec, E.},
title = {Partition-based conditional density estimation},
journal = {ESAIM: Probability and Statistics},
pages = {672--697},
publisher = {EDP-Sciences},
volume = {17},
year = {2013},
doi = {10.1051/ps/2012017},
mrnumber = {3126157},
zbl = {1284.62250},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2012017/}
}
TY - JOUR AU - Cohen, S. X. AU - Le Pennec, E. TI - Partition-based conditional density estimation JO - ESAIM: Probability and Statistics PY - 2013 SP - 672 EP - 697 VL - 17 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2012017/ DO - 10.1051/ps/2012017 LA - en ID - PS_2013__17__672_0 ER -
Cohen, S. X.; Le Pennec, E. Partition-based conditional density estimation. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 672-697. doi : 10.1051/ps/2012017. http://www.numdam.org/articles/10.1051/ps/2012017/
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