Author(s)

Whitney V. Worley¹, Dean M. Young², Phil D. Young³

¹Department of Mathematics, University of Central Arkansas, Conway, AR, USA.
²Department of Statistical Science, Baylor University, Waco, TX, USA.
³Department of Information Systems and Business Analytics, Baylor University, Waco, TX, USA.

We consider the efficacy of a proposed linear-dimension-reduction method to potentially increase the powers of five hypothesis tests for the difference of two high-dimensional multivariate-normal population-mean vectors with the assumption of homoscedastic covariance matrices. We use Monte Carlo simulations to contrast the empirical powers of the five high-dimensional tests by using both the original data and dimension-reduced data. From the Monte Carlo simulations, we conclude that a test by Thulin [1], when performed with post-dimension-reduced data, yielded the best omnibus power for detecting a difference between two high-dimensional population-mean vectors. We also illustrate the utility of our dimension-reduction method real data consisting of genetic sequences of two groups of patients with Crohn’s disease and ulcerative colitis.

Homoscedastic Covariance Matrices, Test Power, Monte Carlo Simulation, Moore-Penrose Inverse, Singular Value Decomposition

Worley, W. , Young, D. and Young, P. (2021) Dimension Reduction for Detecting a Difference in Two High-Dimensional Mean Vectors. Open Journal of Statistics, 11, 243-257. doi: 10.4236/ojs.2021.111013.