通过二元分段多项式选择适应各向异性和不均匀性
Adaptation to anisotropy and inhomogeneity via dyadic piecewise polynomial selection
摘要：
这篇文章致力于通过建立在二进矩形分区上的分段多项式的非线性逼近和估计。研究了可能的非齐次和各向异性光滑类，包含Besov类的逼近率。突出这样的结果在统计学上的兴趣，适应在极大极小意义上的相关的多元密度估计的不均匀性和各向异性证明。此外，该估计过程可以以与样本量简单线性的计算复杂性来实现。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
