TITLE:
Dimension Reduction for Detecting a Difference in Two High-Dimensional Mean Vectors
AUTHORS:
Whitney V. Worley, Dean M. Young, Phil D. Young
KEYWORDS:
Homoscedastic Covariance Matrices, Test Power, Monte Carlo Simulation, Moore-Penrose Inverse, Singular Value Decomposition
JOURNAL NAME:
Open Journal of Statistics,
Vol.11 No.1,
February
26,
2021
ABSTRACT: 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.