On specification error in the general linear model and weak mean square error superiority of the mixed estimator
The case of applying mixed estimation to a general linear model that is misspecified due to missing relevant explanatory variables is investigated. It is found that when the prior information is unbiased and independent of the sample information, the mixed estimator is not necessarily weak mean square error superior to the ordinary least squares estimator of the parameters of the model. In fact, the mixed model using the unbiased prior information can accentuate the specification bias.