Spatially adaptive density estimation by localised Haar projections
Spatially adaptive density estimation by localised Haar projections
复制标题
通过局部 Haar 投影进行空间自适应密度估计
DOI：
10.1214/12-aihp485
复制
发表时间：
2011
影响因子：
1.5
通讯作者：
V. Spokoiny
中科院分区：
文献类型：
--
作者：
F. Gach;Richard Nickl;V. Spokoiny
给定一个来自未知密度f0：R]的随机样本，我们设计了f0的Haar小波估计，其分辨率水平是从局部化测试程序中构建的（如Lepski，Mammen，and Spokoiny（1997，Ann. Statistist.））。我们表明，这些估计适应空间异质平滑的f0，同时为每一个点x在一个固定的间隔，在超范数损失。在实际中，在真密度在估计点x的邻域内是局部常数的理想化假设下，可以选择测试过程中所涉及的阈值常数，并给出了这种做法的信息论justi阳离子。
Given a random sample from some unknown density f0 : R → [0;∞) we devise Haar wavelet estimators for f0 with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen, and Spokoiny (1997, Ann. Statist.)). We show that these estimators adapt to spatially heterogeneous smoothness of f0, simultaneously for every point x in a fixed interval, in sup-norm loss. The thresholding constants involved in the test procedures can be chosen in practice under the idealised assumption that the true density is locally constant in a neighborhood of the point x of estimation, and an information theoretic justi cation of this practice is given.