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Inference on 3D Procrustes Means: Tree Bole Growth, Rank Deficient Diffusion Tensors and Perturbation Models
Author(s) -
HUCKEMANN STEPHAN
Publication year - 2011
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2010.00724.x
Subject(s) - mathematics , perturbation (astronomy) , inference , rank (graph theory) , diffusion mri , procrustes analysis , central limit theorem , pure mathematics , statistical physics , statistics , mathematical analysis , combinatorics , geometry , artificial intelligence , medicine , physics , quantum mechanics , computer science , magnetic resonance imaging , radiology
. 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.