A test for variance-covarianch parameters in normal linear models

Abstract

This paper derives a test statistic for the variance-covariance parameters which is a quadratic function of their MINQUE (Minimum Norm Quadratic Unbiased Estimation) estimates. The test is a Wald-type test, and its development closely parallels the theory used to derive a similar test for the coefficients in linear models. In fact, the derivation proceeds by first setting up the estimation problem in a derived linear model in which the dispersion parameters are the coefficients. The test statistic is shown to be the sum of the squares of independent standardized x² variables.

Keywords:

• K²test
• variance-covariance parameters
• minque estimation
• derived linear model
• commutative quadratic subspace