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Partition-based conditional density estimation. (English) Zbl 1284.62250
Summary: We propose a general partition-based strategy to estimate conditional densities with candidate densities that are piecewise constant with respect to the covariates. 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.

MSC:
62G07 Density estimation
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