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Partition-based conditional density estimation

S. X. CohenE. Le Pennec — 2013

ESAIM: Probability and Statistics

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 strategy in which the densities are chosen piecewise conditional according to the variable. We then consider Gaussian mixture...

Adaptive Dantzig density estimation

K. BertinE. Le PennecV. Rivoirard — 2011

Annales de l'I.H.P. Probabilités et statistiques

The aim of this paper is to build an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Candès and Tao’s approach, we propose a minimization of the 1-norm of the coefficients in the linear combination under an adaptive Dantzig constraint coming from sharp concentration inequalities. This allows to consider a wide class of dictionaries. Under local or global structure assumptions, oracle inequalities are derived. These theoretical results are transposed...

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