Some results in estimation and tests of linear hypotheses under the gauss-markoff model

Abstract

A number of results, hitherto unrecorded in the literature, on the Gauss-Markoff (G-M) model, are discussed. Explicit expressions for BLU estimators of linear parametric functions, covariance matrix of BLUE's and test criteria for tests of linear hypotheses are obtained in the case when the observations have a singular covariance matrix. These are obtained by first reducing a G-M model with a singular covariance matrix to one with a nonsingular covariance matrix and with some restrictions on the parameters, and then applying the known theory in the latter case. Some results in Linear Algebra which are of general interest and which are particularly useful in the discussions on inference from linear models, are also given. Finally some comments are made on the use of Householder transformation in the numerical computation of BLUE's and test criteria.