%0 Journal Article
%T Dimension Reduction for Detecting a Difference in Two High-Dimensional Mean Vectors
%A Whitney V. Worley
%A Dean M. Young
%A Phil D. Young
%J Open Journal of Statistics
%P 243-257
%@ 2161-7198
%D 2021
%I Scientific Research Publishing
%R 10.4236/ojs.2021.111013
%X 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.
%K Homoscedastic Covariance Matrices
%K Test Power
%K Monte Carlo Simulation
%K Moore-Penrose Inverse
%K Singular Value Decomposition
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=107499