Efficiency of generalized least squares estimator with applications to AR(1), sur and heteroscedastic models

The multiple linear regression model and its estimation using ordinary least squares (OLS) is doubtless the most widely used tool in statistics. It allows to estimate the relation between a dependent variable and a set of explanatory variables. Generally, it is seen that the classical conditions need not hold in practice. Although these classical conditions have no effect on the OLS method, they do affect the properties of the OLS estimators and resulting test statistics. In particular, when the elements of y have unequal variances and/or are correlated, var(y) is no longer a scalar variance-covariance matrix and hence there is no guarantee that the OLS estimator is the most efficient within the class of linear unbiased (or the class of unbiased) estimators. In practice, we hardly know the true properties of y. It is therefore important to consider estimation that is valid when var(y) has a more general form. In this thesis, the method of generalized least squares (GLS) is introduced to improve upon estimation efficiency when var(y) is not a scalar variance-covariance matrix and its applications to seemingly unrelated regression (SUR) and heteroscedastic models are analyzed.