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Abstract:
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Consider matrix-variate data X, for which the covariance of vec(X) can be decomposed into a Kronecker product of matrices A and B. Suppose the samples are divided into two groups, and we are interested in estimating the differences in group means for each variable. We present two methods based on generalized least squares for estimating the mean structure as well as covariance matrices in this setting. The first method is based on group centering of each column of X before estimating the row wise covariance matrix B. The second method uses an intricate model selection step which allows us to perform group centering only on genes with sufficiently large effect size, while leaving others to the usual (default) global centering procedure. We provide rates of convergence on mean and covariance estimation with respect to the sample size f, the number of genes m, and the number of genes with a significant effect size, which characterizes the sparsity parameter in our problem. Our analysis applies to a model where the marginals of each row and column vectors follow subgaussian distribution under the same mean structure.
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