A likelihood test for multivariate serial correlation
Peter C. O'Brien · Biometrika · 1980
A procedure is proposed for testing the hypothesis that a sequence of vector-valued random variables is mutually independent. The test is based on the likelihood criterion for first-order autocorrelation assuming a multivariate normal distribution, is simple computationally, and provides a multivariate generalization of the serial correlation coefficient. The distribution of the test statistic is found to be closely approximated by an F distribution, even in samples of size 10 from an exponential distribution, with the approximation holding exactly asymptotically for any underlying distribution with finite fourth moments. This procedure was originally developed for the problem of testing for time-space clustering in a study, discussed in this paper, of leukaemia.