COVARIANCE MATRIX ESTIMATION IN LINEAR MODELS,

In regression analysis with heteroscedastic andor correlated errors, the usual assumption is that the covariance matrix of the errors is completely specified, except perhaps for a scalar multiplier. This condition is relaxed in this paper by assuming only that the covariance matrix has a certain pattern for example, that the covariance matrix is diagonal or partitionable into a diagonal matrix of sub-matrices. The method used for estimating the covariance matrix 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. Author