POWER COMPARISON OF SOME TESTS FOR DETECTING A CHANGE IN THE MULTIVARIATE MEAN

Abstract

Using Monte Carlo methods, we compare the power of three tests based on each of N ≥ 2 p-dimensional random vectors x 1,…,x N to decide if the means μi of the x i's are all equal against the alternative that a change has occurred at some point r (i.e., μ1 = μ2 = ··· = μ r ≠ μ r+1 = μ N ). The vectors x i are assumed to have multivariate normal distributions with common unknown covariance matrix Σ. Two of these tests, a likelihood ratio test and a generalization of Bayes test have been proposed by Srivastava and the third test is a generalization of a test proposed by Sen and Srivastava. It is found that for detecting moderate to large shifts, the test based on the LR statistics performs best when the change occurs near the beginning or the end, while the generalization of Sen and Srivastava's test performs best when the change occurs near the middle. A third test, a multivariate generalization of a univariate Bayes test is slightly inferior. However, for detecting small shifts, or for large sample sizes (N≥60) and moderate p, all three tests perform similarly in the cases we considered. The sequential stopping rule along with pinching-algorithm of Dunn are used to provide tables of simulated percentiles.