This works by using uniroot to find the appropriate \(\rho\) which sets the derivative of the log-likelihood to zero for the AR and CS options - it is not fast but if this is the true structure it will be better in some sense than an unstructured variance matrix. For more details about matrix variate distributions in general and matrix variate normal distributions in particular, see Gupta and Nagar ( 1999), whose results I rely on for much of this presentation.Ī random matrix \(\mathbf\) are possible with row.variance and col.variance commands. This package presents some functions for doing so in the case of matrix variate normal distributions. We may be interested in drawing from such distributions, calculating densities, or estimating parameters based on observations.
One case where this might come up is a multivariate time series: at each point in time we are dealing with a multivariate observation (perhaps normally distributed or not) and then there is a covariance structure across time to account for. Suppose there is a two-dimensional grid of observations: each observation is randomly distributed somehow, perhaps each spot on the grid has its own mean, there’s a covariance relation across the rows that doesn’t vary across the columns and a covariance relation across the columns that doesn’t vary across the rows.
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