Estimation-Equivalent and Dispersion-Equivalent Error Covariance Matrices for the General Linear Model

Abstract

SYNOPTIC ABSTRACTWe give a new, very concise derivation of an explicit characterization representation of the general nonnegative-definite error covariance matrix for a Gauss-Markov model, such that the best linear unbiased estimator is identical to the least-squares estimator. Our characterization derivation is very concise, and we use only elementary matrix properties in the proof. We also characterize the general symmetric nonnegative-definite error covariance matrix of a Gauss-Markov model, such that the covariance matrices of the best linear unbiased estimator, the least squares estimator, and the independently and identically-distributed least-squares estimator have identical covariance structures.