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

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

2010-02-03

arxiv.org/abs/1002.0738v2

Statistics

Methodology

27 pages, 4 figures

Scientific paper

The Central Limit Theorem (CLT) for extrinsic and intrinsic means on manifolds is extended to a generalization of Fr\'echet 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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