Improved Multivariate Prediction in a General Linear Model with an Unknown Error Covariance Matrix

This paper deals with the problem of Stein-rule prediction in a general linear model. Our study extends the work of Gotway and Cressie (1993) by assuming that the covariance matrix of the model's disturbances is unknown. Also, predictions are based on a composite target function that incorporates allowance for the simultaneous predictions of the actual and average values of the target variable. We employ large sample asymptotic theory and derive and compare expressions for the bias vectors, mean squared error matrices, and risks based on a quadratic loss structure of the Stein-rule and the feasible best linear unbiased predictors. The results are applied to a model with first order autoregressive disturbances. Moreover, a Monte-Carlo experiment is conducted to explore the performance of the predictors in finite samples.