Multivariate regression with consecutively added dependent variables

We consider multivariate regression where new dependent variables are consecutively added during the experiment (or in time). So, viewed at the end of the experiment, the number of observations decreases with each added variable. The explanatory variables are observed throughout. In this paper the classic estimation and testing theory for the complete multivariate regression model is extended for this incomplete model. These extensions are far from trivial. With regard to estimation, OLS and GLS no longer coincide. Therefore EGLS with various choices for the estimators of the covariance matrix is discussed. In case of normality it appears that ML coincides with EGLS for a specific (complicated) choice. With regard to testing, (generalized) MANOVA-tables are presented. In case of normality they are used for exact LR-tests on the regression coefficients, using a generalization of the Wilks’ distribution. In our analysis we emphasize a geometric approach, thereby avoiding tedious matrix calculations.