Improved estimation for dynamic linear regression model

This paper studies the preliminary test and shrinkage estimators based on the Kalman filtering procedure applied to a dynamic linear state space regression model. The performance of these estimators, with respect to mean square error, was investigated. It was revealed that under certain conditions both the preliminary test and shrinkage estimators proposed outperform the Kalman filter. This out-performance was not uniform. Further, the shrinkage estimator was found to be superior to the preliminary test estimator over large regions. The results presented in this paper invalidates the global minimum mean square error property of the Kalman filter that is widely used by the engineers for estimation of the parameters of linear state space models.