In this note, the basic lemma of the linear identification problem is revisited. By utilizing a joint decomposition of orthogonal projectors as partitioned matrices, a new proof of the lemma is proposed. From the algebraic point of view, the present proof might be the simplest from among all...

We consider Bayesian estimation of the coefficients in a linear regression model, using a conjugate prior, when certain additional exact restrictions are placed on these coefficients. The bias and matrix mean squared errors of the Bayes and restricted Bayes estimators are compared when these...

We consider estimating the linear regression model’s coefficients when there is uncertainty about coefficient restrictions. Theorems establish that the mean squared errors of combination estimators, formed as weighted averages of the ordinary least squares and one or more restricted least...

The problem of testing a set of restrictions R(q)=0 in a complex hierarchical model is considered. We propose a different approach from the standard PO ratio test, which can be viewed as the Bayesian analogous to the classical Wald type test. With respect to the PO ratio, it has the advantage of...