Transformations for Estimation of Linear Models with Nested-Error Structure

TLDR: In this article, two linear models with error structure of the nested type are considered and transformations are presented by which uncorrelated errors with constant variances are obtained, where the transformed observations are differences between the original observations and multiples of averages of subsets of the observations.

Abstract: Two linear models with error structure of the nested type are considered. Transformations are presented by which uncorrelated errors with constant variances are obtained. The transformed observations are differences between the original observations and multiples of averages of subsets of the observations. The transformations permit the calculation of the generalized least-squares estimators and their covariance matrices by ordinary least-squares regression. Regression-type estimators are presented for use when the variance components are unknown. Sufficient conditions are presented under which the estimated generalized least-squares estimator is unbiased and asymptotically equivalent to the generalized least-squares estimator.