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Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection. (English) Zbl 1308.62070
Summary: 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.

MSC:
62G07 Density estimation
62H12 Estimation in multivariate analysis
41A15 Spline approximation
41A63 Multidimensional problems
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