Abstract:
|
This paper develops a nonparametric a k-sample test on shape space. The fact that shape space is non-Euclidean, and sometimes infinite-dimensional, rules out standard ANOVA and requires new ideas. We advance a metric-based approach called DISCO analysis, originally developed for Euclidean space in Rizzo and Szekely (2010), and apply it to the shape space of planar closed curves. This adaptation leads to a statistic for testing equality of distributions of groups. A theoretical proof for this approach is given under Full Procrustes metric in Kendell's shape space. We illustrate our method with mitochondrial boundaries. The goal is to test whether factors--mitochondria type (SS/IMF), cell label or exercise (sedentary/running), affect the mitochondrial morphology as imaged from skeletal muscles of mice. Since the data has a nested structure, we also develop a procedure to test a factor while it contains another significant factor. Experimental studies under 5 shape metrics are given. The results generally agree with past studies on mitochondrial morphology, but we additionally discover the significance of factor exercise for SS mitochondria under the scaled elastic shape metric.
|