Some Further Notes on Disturbance Estimates in Regression Analysis

For the well-known general linear model Theil has recently developed the so-called best linear disturbance estimates with a covariance matrix equal to σ2 I. In this article we give a slightly different formulation of his problem which may give us some more insight in this estimation procedure. An important check on the computations of these estimates is given, as well as a comparison of these estimates with the commonly used least-squares estimates. For some special cases the BLUS estimates are analytically derived. The BLUS estimates are important for research workers who deal with time series because these estimates can be used to test auto-correlation among the disturbances.