Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection

Details Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection

2011-02-15

arxiv.org/abs/1102.3108v1

Mathematics

Statistics Theory

Scientific paper

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.

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