Abstract: In a regression setting, the greatest lower bound for the largest eigenvalue of the covariance matrix of the generalized least squares estimator when the experimental errors are correlated is derived under the experimental region considered by Chan and Li (1989). A neat and efficient algorithm for constructing an E-optimal design matrix via a CL vector is then achieved. It is also shown that for the E-optimal design matrix the generalized least squares and the ordinary least squares estimators are identical, and thus the two estimators have the same E-optimal design matrix.
Key words and phrases: A-optimal design, CL vector, correlated error, E-optimal design, generalized least squares, majorization, ordinary least squares.