基于Needlets的单位球面上局部自适应密度估计
Locally Adaptive Density Estimation on the Unit Sphere Using Needlets
摘要：
考虑了利用Needlet标架从方向数据估计（d-1）维单位球面S^{d-1}上的概率密度函数f的问题。它表明，needlet系数的衰减支持附近的一个点的函数f只依赖于局部的Hölder连续性的f在x。然后，这是用来表明，在Baldi，Kerkyacharian，Marinucci和Picard引入的阈值needlet估计适应局部正则性的f。此外，基于阈值needlet估计，提出了一个自适应的置信区间的f，这是渐近诚实的适当类的局部Hölderian密度。
英文摘要：
The problem of estimating a probability density function f on the (d-1)-dimensional unit sphere S^{d-1} from directional data using the needlet frame is considered. It is shown that the decay of needlet coefficients supported near a point of a function f depends only on local Hölder continuity properties of f at x. This is then used to show that the thresholded needlet estimator introduced in Baldi, Kerkyacharian, Marinucci and Picard adapts to the local regularity properties of f. Moreover an adaptive confidence interval for f based on the thresholded needlet estimator is proposed, which is asymptotically honest over suitable classes of locally Hölderian densities.
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