Physical Sciences and Mathematics Commons^™

Permutation Testing For Covariance Matrices, With Applications In Shape Analysis, Blake Cassidy Hill

Theses and Dissertations

In many applications, it is of interest to compare covariance structures. In this work, we propose hypothesis tests for comparing covariance matrices for data in different groups, especially in shape analysis. The main motivation for the work is comparing covariance matrices of the size and shapes of damaged versus undamaged DNA molecules. A practical motivation behind analyzing the differences between these DNA covariance matrices is to compare the variation between the two groups during situations where the molecules are repairing. The testing methods proposed in this dissertation consist of three types of permutation testing methods for differences in covariance structures. …