Asymptotics of 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 a previous paper we determined the least squares and maximum likelihood estimators for the parameters in this model. In this paper, we discuss the estimation technique of iterative least squares to calculate the maximum likelihood estimates and we prove the consistency of the estimators in each iteration. Moreover, we introduce a general class of estimators for the regression parameters based on arbitrary starting estimators for the covariance matrix. We prove the consistency of these new estimators and - for sake of completeness - of the previously obtained least squares and maximum likelihood estimators as well