  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.
