Nonparametric method for sparse conditional density estimation in moderately large dimensions

Minh-Lien Jeanne Nguyen (1, 2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 SELECT - Model selection in statistical learning

In this paper, we consider the problem of estimating a conditional density in moderately large dimensions. Much more informative than regression functions, conditional densities are of main interest in recent methods, particularly in the Bayesian framework (studying the posterior distribution, finding its modes...). Considering a recently studied family of kernel estimators, we select a pointwise multivariate bandwidth by revisiting the greedy algorithm Rodeo (Regularisation Of Derivative Expectation Operator). The method addresses several issues: being greedy and computationally efficient by an iterative procedure, avoiding the curse of high dimensionality under some suitably defined sparsity conditions by early variable selection during the procedure, converging at a quasi-optimal minimax rate.

Mots clés: greedy algorithm; nonparametric inference; kernel density estimators; minimax rates; conditional density; high dimension; sparsity

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Méthodologie [stat.ME]

Minh-Lien Jeanne Nguyen. Nonparametric method for sparse conditional density estimation in moderately large dimensions. 2018. ⟨hal-01688664⟩