Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection

Nathalie Akakpo (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

This article is devoted to nonlinear approximation and estimation via piecewise polynomials built on partitions into dyadic rectangles. The approximation rate is studied over possibly inhomogeneous and anisotropic smoothness classes that contain Besov classes. Highlighting the interest of such a result in statistics, adaptation in the minimax sense to both inhomogeneity and anisotropy of a related multivariate density estimator is proved. Besides, that estimation procedure can be implemented with a computational complexity simply linear in the sample size.

Keywords: Anisotropic Besov spaces; Density estimation; Multivariate estimation; Spatial adaptation; Nonlinear approximation

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]; Classical Analysis and ODEs [math.CA]; Functional Analysis [math.FA]

Nathalie Akakpo. Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection. 2011. ⟨hal-00565918⟩