Some results for a superiority problem in misspecified restricted linear models

Razzaghi (1987) conjectured that a wrong choice of covariance matrix in a restricted linear model results in loss of efficiency. This conjecture was proved correct by Kabe and Gupta (1989) for a wrong choice of constant covariance matrix. The present paper demonstrates that this loss of efficiency persists even with an estimated covariance matrix, thereby resulting in inefficient estimation, prediction, and confidence intervals.