三维Procrustes平均值的推导：树干生长、秩亏扩散张量和扰动模型
Inference on 3D Procrustes means: tree bole growth, rank-deficient diffusion tensors and perturbation models
摘要：
将流形上的外平均和内平均的中心极限定理推广到Fréchet平均的推广.例子是3D肯德尔形状的Procrustes平均值以及Ziezold引入的平均值。这允许单样本测试以前不可能的，并在数值上评估的“不一致的Procrustes平均值”的扰动模型和“不一致”的模型内最近提出的扩散张量成像。此外，它表明，CLT可以扩展到轻度秩亏扩散张量。应用到林业给出了时间演变的花旗松树干倾向于强烈的圆柱体在早期的年龄和倾向于增加竞争。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
