Large sample theory of intrinsic and extrinsic sample means on manifolds - II
Large sample theory of intrinsic and extrinsic sample means on manifolds - II
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DOI：
10.1214/009053605000000093
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发表时间：
2005-06-01
影响因子：
4.5
通讯作者：
Patrangenaru, V
中科院分区：
文献类型：
--
作者：
Bhattacharya, R;Patrangenaru, V
本文发展了流形上均值的估计和检验问题的非参数推理程序。导出了Frechet样本均值的中心极限定理，从而导出了黎曼流形上内在样本均值的渐近分布理论。中心极限定理也获得了外部样本的手段w.r.t.欧氏空间中可微流形的任意嵌入。特别适合于这些问题的Bootstrap方法。应用于球面Sal（方向空间）、真实的射影空间Rp（N-1）（轴空间）、复射影空间Cpk-2（平面形状空间）上的分布。Veronese-Whitney嵌入和三维形状空间Sigma（4）（3）.
This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Frechet sample means is derived leading to an asymptotic distribution theory of intrinsic sample means on Riemannian manifolds. Central limit theorems are also obtained for extrinsic sample means w.r.t. an arbitrary embedding of a differentiable manifold in a Euclidean space. Bootstrap methods particularly suitable for these problems are presented. Applications are given to distributions on the sphere Sal (directional spaces), real projective space Rp(N-1) (axial spaces), complex projective space Cpk-2 (planar shape spaces) w.r.t. Veronese-Whitney embeddings and a threedimensional shape space Sigma(4)(3).