Permutation Testing for Covariance Matrices, with Applications in Shape Analysis

• Activity Number: 378
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Hao Wang*+
• Companies: Michigan State University

Abstract

We propose hypothesis tests for comparing covariance matrices for shape data arising from two different groups. The main scientific motivation is the comparison between the shapes of damaged versus undamaged DNA molecules. We propose three types of permutation testing procedures under three scenarios: the equal mean shapes between groups, the unequal mean shapes between groups, and the temporally dependent shapes. We evaluate these tests for a number of metrics between covariance matrices and demonstrate that they have good performance. We apply the new methods to a DNA dataset and a rat calvarial growth dataset.