A Central Limit Theorem for extrinsic antimeans and estimation of Veronese-Whitney means and antimeans on planar Kendall shape spaces

JOURNAL OF MULTIVARIATE ANALYSIS

卷:178

Article

Wang, Yunfan¹  Patrangenaru, Vic¹  Guo, Ruite¹ 

[1] Florida State Univ, Dept Stat, Tallahassee, FL 32306 USA

关键词: Complex projective space;    Extrinsic antimean;    Kendall planar shape space;    Nonparametric bootstrap;    Random object;    Statistics on manifolds;    Veronese Whitney embedding;   

DOI  :  10.1016/j.jmva.2020.104600

来源: Elsevier

【 摘 要 】

This article is concerned with random objects in the complex projective space CPk-2. It is shown that the Veronese-Whitney (VW) antimean, which is the extrinsic antimean of a random point on CPk-2 relative to the VW-embedding, is given by the point on CPk-2 represented by the eigenvector corresponding to the smallest eigenvalue of the expected mean of the VW-embedding of the random point, provided this eigenvalue is simple. We also derive a CLT for extrinsic sample antimeans, and an asymptotic chi(2)-distribution of an appropriately studentized statistic, based on the extrinsic antimean, which in the particular case of a VW-embedding is then used to construct nonparametric bootstrap confidence regions for the VW-antimean planar Kendall shape. Simulations studies and an application to medical imaging are illustrating the proposed methodology. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free