Journal
ANNALS OF STATISTICS
Volume 39, Issue 2, Pages 1098-1124Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/10-AOS862
Keywords
Geodesic principal components; Ziezold mean; asymptotic inference; strong consistency; central limit theorem; shape analysis; forest biometry; geodesic; parallel hypothesis
Categories
Funding
- DFG [MU 1230/10-1]
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For planar landmark based shapes, taking into account the non-Euclidean geometry of the shape space, a statistical test for a common mean first geodesic principal component (GPC) is devised which rests on one of two asymptotic scenarios. For both scenarios, strong consistency and central limit theorems are established, along with an algorithm for the computation of a Ziezold mean geodesic. In application, this allows to verify the geodesic hypothesis for leaf growth of Canadian black poplars and to discriminate genetically different trees by observations of leaf shape growth over brief time intervals. With a test based on Procrustes tangent space coordinates, not involving the shape space's curvature, neither can be achieved.
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