Relation between pearsonian cofficients of distribution of lease squares estimators and the disturbance term

Abstract

It is well known that distribution of ordinary least squares (OLB) estimators of parameters in a general regression model depends upon the distribution followed by the associated disturbance term though the method itself does not require any such assumption. Accordingly, properties of the two distributions could be compared only if one assigns, a priori, some distributional form to the unknown disturbance term. It is, however, possible to establish a relation, in general, between the Pearsonian coefficients of distributions of OLB estimators and the disturbance term even without making any assumption regarding distribution of the latter. The present note provides a relationship between {31 and {32 (Pearsonian) coefficients corresponding to the two distributions. In Theorem 1, we derive third and fourth moments of OLB estimators and then use these results to prove Theorem 2.