Non compact estimation of the conditional density from direct or noisy data

Fabienne Comte (1) , Claire Lacour (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 LAMA - Laboratoire Analyse et de Mathématiques Appliquées

In this paper, we propose a nonparametric estimation strategy for the conditional density function of Y given X, from independent and identically distributed observations (Xi, Yi) 1≤i≤n. We consider a regression strategy related to projection subspaces of L 2 generated by non compactly supported bases. This rst study is then extended to the case where Y is not directly observed, but only Z = Y + ε, where ε is a noise with known density. In these two settings, we build and study collections of estimators, compute their rates of convergence on anisotropic space on non-compact supports, and prove related lower bounds. Then, we consider adaptive estimators for which we also prove risk bounds.

Mots clés: Anisotropic Sobolev spaces; Conditional density; Deconvolution; Hermite basis; Laguerre basis; Noisy data; Nonparametric estimation AMS 2020 Classication; 62G05-62G07-62G08

Domaines: Statistiques [math.ST]

Fabienne Comte, Claire Lacour. Non compact estimation of the conditional density from direct or noisy data. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2023, 59 (3), pp.1463-1507. ⟨10.1214/22-AIHP129⟩. ⟨hal-03276251⟩