Problem Formulation and Main Results
The GMANOVA model was first formulated by Potthoff and Roy [1], who were interested in fitting the following patterned-mean problem: , where is a data matrix whose columns are independent random vectors with common covariance matrix , and are known matrices, and is a matrix of unknown regression coefficients. In [1], this model was applied to fitting growth patterns of groups of individuals, hence also the name growth-curve model [1]–[8]. (Other common statistical applications are: clinical trials of pharmaceutical drugs, agronomical investigations, and business surveys; see [6]–[9] for illustrative examples.) In [2], Khatri computed maximum likelihood (ML) estimates of and under the multivariate normal model for . Khatri's results are closely related to the concomitant-variable method, independently developed by Rao [3], [4]. In [68], it was shown that the estimates of the regression coefficients and corresponding generalized likelihood ratio tests developed in [2] are robust when the errors are not normal.