Deconvolution density estimation on SO(N)
Deconvolution density estimation on SO(N)
复制标题
SO(N) 的反卷积密度估计
DOI：
10.1214/aos/1024691089
复制
发表时间：
1998
影响因子：
4.5
通讯作者：
P. Kim
中科院分区：
文献类型：
--
作者：
P. Kim
本文发展了SO(N)的非参数反卷积密度估计，SO(N)是N × N个行列式为1的正交矩阵群。方法是利用群和流形结构使欧几里得反卷积技术适应这种李群环境。这是通过采用显式SO(N)的群表示理论来实现的，在充分的平滑条件下，获得了具有特定收敛率的一般一致性结果。并讨论了在经验贝叶斯先验估计和推理中的应用。
This paper develops nonparametric deconvolution density estimation over SO(N), the group of N x N orthogonal matrices of determinant 1. The methodology is to use the group and manifold structures to adapt the Euclidean deconvolution techniques to this Lie group environment. This is achieved by employing the theory of group representations explicit to SO(N), General consistency results are obtained with specific rates of convergence achieved under sufficient smoothness conditions. Application to empirical Bayes prior estimation and inference is also discussed.