Nonparametric estimation of conditional densities: high dimensionality, parsimony and gluttonous algorithms.

Summary We consider the problem of estimating conditional densities in moderately high dimensions. Much more informative than regression functions, conditional densities are of major interest in recent methods, especially in the Bayesian framework (study of the posterior distribution, search for its modes.). After recalling the problems related to high-dimensional estimation in the introduction, the next two chapters develop two methods that tackle the scourge of dimension by requiring: to be computationally efficient thanks to a gluttonous iterative procedure, to detect the relevant variables under a parsimony assumption, and to converge at a near-optimal minimax speed. More precisely, both methods consider kernel estimators well adapted to the estimation of conditional densities and select a point multivariate window by revisiting the gluttonous RODEO (Re- gularisation Of Derivative Expectation Operator) algorithm. The first method has ini- tialization problems and additional logarithmic factors in the speed of convergence, the second method solves these problems, while adding regularity adaptation. In the penultimate chapter, we discuss the calibration and numerical performance of these two procedures, before giving some comments and perspectives in the last chapter.