Multiple comparisons of several heteroscedastic multivariate populations

This paper presents several statistics appearing in multiple comparisons of heteroscedastic multivariate populations. Due to the very slow convergence of these statistics to their limiting distributions, the large sample Bonferroni or DL-based procedures reveal poor coverage probabilities even in the normal case. Thus, the second-order asymptotic expansions with estimated cumulants are applied to improve their coverage probabilities. A large simulation study illustrates the performance of the second-order corrected procedures.