A parametric bootstrap solution to the MANOVA under heteroscedasticity

K. Krishnamoorthy, Fei Lu
2010 Journal of Statistical Computation and Simulation  
In this article, we consider the problem of comparing several multivariate normal mean vectors when the covariance matrices are unknown and arbitrary positive definite matrices. We propose a parametric bootstrap (PB) approach, and develop an approximation to the distribution of the PB pivotal quantity for comparing two mean vectors. This approximate test is shown to be the same as the invariant test given in Krishnamoorthy and Yu (2004, Statistics & Probability Letters, 66, 161-169) for the
more » ... 61-169) for the multivariate Behrens-Fisher problem. Furthermore, we compare the PB test with two existing invariant tests via Monte Carlo simulation. Our simulation studies show that the PB test controls the Type I error rates very satisfactorily while other tests are liberal especially when the number of means to be compared is moderate and/or sample sizes are small. The tests are illustrated using an example.
doi:10.1080/00949650902822564 fatcat:atrlqgreqbhsrkgxw3h2n4bddu