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.
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