Exact results on the inadmissibility of the feasible generalized least squares estimator in regression models with non-spherical disturbances

In various guises, feasible generalized least squares (FGLS) estimation has occupied an important place in regression analysis for more than 35 years. Past studies on the characteristics of the FGLS estimators are largely based on large sample evaluations, and the important issue of admissibility remains unexplored in the case of the FGLS estimator. In this paper, an exact sufficient condition for the dominance of a Stein-type shrinkage estimator over the FGLS estimator in finite samples based on squared error loss is given. In deriving the condition, we assume that the model's disturbance covariance matrix is unknown except for a scalar multiple. Further, for models with AR(1) disturbances, it is observed that the dominance condition reduces to one that involves no unknown parameter. In other words, in the case of AR(1) disturbances and where the condition for risk dominance is met, the FGLS estimator is rendered inadmissible under squared error loss.