Asymptotic equivalence for density estimation and Guassian white noise: an extension

Ester Mariucci (1)

1 IPS - Inférence Processus Stochastiques

The aim of this paper is to present an extension of the well-known asymptotic equivalence between density estimation experiments and a Gaussian white noise model. Our extension consists in enlarging the nonparametric class of the admissible densities. More precisely, we propose a way to allow densities defined on any subinterval of R, and also some discontinuous or unbounded densities are considered (so long as the discontinuity and unboundedness patterns are somehow known a priori). The concept of equivalence that we shall adopt is in the sense of the Le Cam distance between statistical models. The results are constructive: all the asymptotic equivalences are established by constructing explicit Markov kernels.

Mots clés: asymptotic equivalence; asymptotic minimax risk; deficiency distance; Nonparametric experiments

Domaines: Probabilités [math.PR]; Statistiques [stat]; Analyse numérique [math.NA]

Ester Mariucci. Asymptotic equivalence for density estimation and Guassian white noise: an extension. 2015. ⟨hal-01132442v1⟩