Covariance Matrix Estimation in Linear Models

Abstract In regression analysis with heteroscedastic and/or correlated errors, the usual assumption is that the covariance matrix σ of the errors is completely specified, except perhaps for a scalar multiplier. This condition is relaxed in this paper by assuming only that σ has a certain pattern; for example, that σ is diagonal or partitionable into a diagonal matrix of sub-matrices. The method used for estimating σ is the standard procedure of equating certain quadratic forms of the observations (in this case, squares and products of residuals from regression) to their expectations, and solving for the unknown variances and covariances. A numerical example illustrates the method.