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piecewise polynomial density

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1 results

Partition-based conditional density estimation
S. X. Cohen, E. Le Pennec
Journal:

ESAIM: Probability and Statistics / Volume 17 / 2013

Published online by Cambridge University Press:

04 November 2013, pp. 672-697

Print publication:

2013
- Article
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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.