ABSTRACT
This chapter introduces C. R. Rao's least squares unified theory. Several two-stage estimators for estimation of parameters in Seemingly Unrelated Regression models have been proposed to improve the least squares estimators. Since the 1960's, the study of parameter estimation in singular linear model has become very active. Many estimation procedures have been proposed R. M. Pringle and A. A. Rayner, and A. Albert. The unified method of least squares and the method of an inverse partitioned matrix proposed by Rao have received much attention and have extensive applications. Rao introduced the use of the g-inverse of the partitioned matrix in the estimation of singular linear models. This method is referred to as the inverse partitioned matrix method. A statistical inference is usually obtained based upon the observations under some distribution or model assumptions. The assumptions regarding the underlying distribution or model can certainly have an impact on the statistical inference.
