Test for Homogeneity of Random Objects on Manifolds with Applications to Biological Shape Analysis

Ruite Guo, Hwiyoung Lee and Vic Patrangenaru ()
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Ruite Guo: Florida State University
Hwiyoung Lee: University of Maryland
Vic Patrangenaru: Florida State University

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 2, No 4, 1178-1204

Abstract: Abstract Methods of testing for the equality of two distributions on a manifold are unveiled in this paper. One defines the extrinsic energy distance associated with two probability measures on a complete metric space embedded in a numerical space. One derives the extrinsic energy statistic test for homogeneity of such distributions. This test is validated via a simulation example on the Kendall space of planar k-ads with a Veronese-Whitney (VW) embedding. Imaging data driven examples are also considered here. In one application, central to the paper, one tests for homogeneity the distributions of planar Kendall shapes of midsections of the Corpus Callosum in a clinically normal population vs a population of ADHD diagnosed individuals; these distributions are not significantly different, although they are known to have highly significant VW-means. On the other hand, in 3D, the reflection shapes of configurations of Acrosterigma Magnum shells are not significantly different, and do not have significantly similar different 3D Schoenberg means.

Keywords: Test for equality of distributions on manifolds; Extrinsic energy statistics; Object data analysis; Nonparametric bootstrap; 3D bioshape analysis from digital camera images; ADHD; Brain imaging; Primary 62R30; 62H35; 62G05. Secondary 62F12; 62P10; 62R99 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13171-023-00310-0

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