Least-Squares Theory Based on General Distributional Assumptions with an Application to the Incomplete Observations Problem

Abstract

The linear regression model y =β′ x + ε is reanalyzed. Taking the modest position that β′ x is an approximation of the “best” predictor of y we derive the asymptotic distribution of b and R 2 , under mild assumptions. The method of derivation yields an easy answer to the estimation of β from a data set which contains incomplete observations, where the incompleteness is random.