Mean Equality Tests for High-Dimensional and Higher-Order Data with k-Self Similar Compound Symmetry Covariance Structure
Abstract
An extension of the D2
test statistic to test the equality of mean for high-dimensional and
k-th order array-variate data using k-self similar compound symmetry (k-SSCS) covariance structure
is derived. The k-th order data appear in many scientific fields including agriculture, medical,
environmental and engineering applications. We discuss the property of this k-SSCS covariance
structure, namely, the property of Jordan algebra. We formally show that our D2
test statistic for k-th
order data is an extension or the generalization of the D2
test statistic for second-order data and for
third-order data, respectively. We also derive the D2
test statistic for third-order data and illustrate
its application using a medical dataset from a clinical trial study of the eye disease glaucoma. The
new test statistic is very efficient for high-dimensional data where the estimation of unstructured
variance-covariance matrix is not feasible due to small sample size.
Department
Management Science and Statistics