University of Washington - Statistics
We consider the problem of testing and estimating separable covariances for relational data sets. We propose to model these data as matrix normal distributions with separate row and column covariance matrices. The existing literature on testing and estimation in the context of a matrix normal distribution requires multiple observations of the matrix, which rarely occurs for relational data sets. We take advantage of the boundedness of the likelihood for a single observation from a square matrix normal distribution to develop a testing procedure for whether or not we need to estimate both row and column covariances. We show that this test has power against multiple alternatives. We then discuss desirable properties of estimators for the row and column covariance matrices and propose several estimators.
We conclude with a discussion of estimating regression coefficients in a model for relational data that exhibits a separable covariance structure.