Likelihood ratio tests for triply multivariate data with structured correlation on spatial repeated measurements

In this article we study the problems of tests of hypotheses on Kronecker product structured covariance matrices with multiple q-variate observations over u sites and over p time/spatial points under the assumption of multivariate normality. We provide the maximum likelihood estimates of the unknown population parameters, and the computation algorithms to calculate the test statistics. The tests are implemented with three real data sets. A simulation study is also performed to check the finite sample performance.