Inference on 3D Procrustes means: tree bole growth, rank-deficient diffusion tensors and perturbation models

2010/02/03 by Stephan Huckemann, Huckemann, Stephan · 2 citations
Engineering · Environmental Science · Mathematics · #FOS: Computer and information sciences #Forest ecology and management #Methodology (stat.ME) #Plant Water Relations and Carbon Dynamics #Tree Root and Stability Studies #stat.ME

paper · pdf · doi:10.48550/arxiv.1002.0738

27 pages, 4 figures

openalex publication_date 2010/02/03 · arxiv created 2011/02/02 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Central Limit Theorem (CLT) for extrinsic and intrinsic means on manifolds is extended to a generalization of Fréchet means. Examples are the Procrustes mean for 3D Kendall shapes as well as a mean introduced by Ziezold. This allows for one-sample tests previously not possible, and to numerically assess the `inconsistency of the Procrustes mean' for a perturbation model and `inconsistency' within a model recently proposed for diffusion tensor imaging. Also it is shown that the CLT can be extended to mildly rank deficient diffusion tensors. An application to forestry gives the temporal evolution of Douglas fir tree stems tending strongly towards cylinders at early ages and tending away with increased competition.

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• Finite Sample Smeariness on Spheres and Modulation-aware Tests
• General M-estimators of location on Riemannian manifolds: existence and uniqueness

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