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Activity Number: 451
Type: Contributed
Date/Time: Tuesday, August 2, 2016 : 3:05 PM to 3:50 PM
Sponsor: Biometrics Section
Abstract #321779
Title: Efficient Mean Structure Estimation Using Matrix Variate Data
Author(s): Michael Hornstein* and Kerby Shedden and Shuheng Zhou
Companies: University of Michigan and University of Michigan and University of Michigan
Keywords: dependent data ; Kronecker product ; correlated samples ; differential expression ; generalized least squares ; transposable data

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.

Authors who are presenting talks have a * after their name.

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