The Analysis of Disturbances in Regression Analysis

Abstract

Classical regression analysis is concerned with the estimation of the parameter vector$beta$of the equation$y = X\beta + u$(1.1)where y is the T-element column vector of values taken by the dependent variable, X the $TxA$ matrix of values taken by the A independent variables, $beta$ a column of A parameters, and u a column of T disturbance.

This article first appeared in the Journal of the American Statistical Association, 60, (1965), 1067-1079. Reprinted with the permission of the American Statistical Association. This research was supported by the National Science Foundation under Grant GS-151 and by the U.S. Army Mathematics Research Center, University of Wisconsin. The author is much indebted to Professor Arnold Zellner and Arthur B. Goldberger of the Social Systems Research Institute and to Dr. J. Barkley Rosser and Mr. H.F. Karreman of the U.S. Army Mathematics Research Center at the University of Wisconsin for their willingness to listen to and comment on his problems. He is also indebted to Mr. C.S. Park of the University of Wisconsin and to Messrs. A Kunstman and J. Koerts of the Econometric Institute, Netherlands School of Economics, who assisted him when completing the paper in Rotterdam. Finally, he wishes to acknowledge some valuable suggestions on exposition and terminology made by several referees.