A0354
Title: Testing of equality of mean submatrices for matrix-variate data under block compound symmetry covariance structure
Authors: Anuradha Roy - The University of Texas at San Antonio (United States) [presenting]
Solomon Harrar - University of Kentucky (United States)
Shouryya Mitra - Xavier University (United States)
Abstract: Observations that are made on p response variables, and each response variable is measured over n sites or time points construct matrix-variate response variables and arise across a wide range of disciplines, including medical, environmental, and agricultural studies. The observations in this matrix-variate sample are not independent but are doubly correlated. A test for equality of mean submatrices is proposed for several groups for matrix-variate data with block compound symmetry (BCS) covariance structure. The test for mean subvectors, also known as the test of additional information, has so far been considered only for independent multivariate (vector-variate) samples. A similar test is pursued for multiple observations of matrix-variate samples under the BCS covariance structure. Specifically, a test statistic is proposed, and its null distribution is studied. Along the way, unbiased estimation is investigated for the parameters and distribution theory for partitioned and Schur-complements of an estimator of BCS covariance matrix. The test statistic is shown to be a convolution of two Lawley-Hotelling trace distributions. Numerical studies show that overall, the proposed test performs quite well when the total sample size is moderate to large relative to the dimension. The practical implications of the methodological aspects of the proposed test of additional information for matrix-variate data are demonstrated using two medical datasets.
