Abstract
In this paper, we consider the general linear hypothesis testing (GLHT) problem in heteroscedastic one-way MANOVA. The well-known Wald-type test statistic is used. Its null distribution is approximated by a Hotelling T2 distribution with one parameter estimated from the data, resulting in the so-called approximate Hotelling T2 (AHT) test. The AHT test is shown to be invariant under affine transformation, different choices of the contrast matrix specifying the same hypothesis, and different labeling schemes of the mean vectors. The AHT test can be simply conducted using the usual F-distribution. Simulation studies and real data applications show that the AHT test substantially outperforms the test of [1] and is comparable to the parametric bootstrap (PB) test of [2] for the multivariate k-sample Behrens-Fisher problem which is a special case of the GLHT problem in heteroscedastic one-way MANOVA.
Highlights
Its null distribution is approximated by a Hotelling T2 distribution with one parameter estimated from the data, resulting in the so-called approximate Hotelling T2 (AHT) test
Simulation studies and real data applications show that the AHT test substantially outperforms the test of [1] and is comparable to the parametric bootstrap (PB) test of [2] for the multivariate k-sample Behrens-Fisher problem which is a special case of the general linear hypothesis testing (GLHT) problem in heteroscedastic one-way multivariate analysis of variance (MANOVA)
The problem of comparing the mean vectors of k multivariate populations based on k independent samples is referred to as multivariate analysis of variance (MANOVA)
Summary
The problem of comparing the mean vectors of k multivariate populations based on k independent samples is referred to as multivariate analysis of variance (MANOVA). Reference [4] essentially showed, via some intensive simulations, that when there is no information about the correctness of the assumption of the equality of the covariance matrices, it is better to directly proceed to make inference using some BF testing procedure which is robust against the violation of the assumption, e.g., using the modified Nel and van der Mere’s (MNV) test proposed by [5]. Other such testing procedures include those proposed by [1,6,7,8,9,10,11], among others.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
