Regression models with unknown singular covariance matrix

AbstractIn the analysis of the classical multivariate linear regression model, it is assumed that the covariance matrix is nonsingular. This assumption of nonsingularity limits the number of characteristics that may be included in the model. In this paper, we relax the condition of nonsingularity and consider the case when the covariance matrix may be singular. Maximum likelihood estimators and likelihood ratio tests for the general linear hypothesis are derived for the singular covariance matrix case. These results are extended to the growth curve model with a singular covariance matrix. We also indicate how to analyze data where several new aspects appear