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

Yunfan Wang, Vic Patrangenaru and Ruite Guo

Journal of Multivariate Analysis, 2020, vol. 178, issue C

Abstract: 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 χ2-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.

Keywords: Complex projective space; Extrinsic antimean; Kendall planar shape space; Nonparametric bootstrap; Random object; Statistics on manifolds; Veronese Whitney embedding (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2020.104600

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