Statistical analysis of a linear regression model with restrictions and superfluous variables

In statistical analysis of regression models, we frequently come across the cases in which two or more competing statistical models are assumed under the given data, while the corresponding statistical inference results are not necessarily the same. In this paper, we consider some comparison problems in the statistical inference of two given competing statistical models, where one is is a true and the other is assumed to be misspecified with inclusion of some superfluous variables. We shall derive the best linear unbiased estimators of unknown parametric vectors under the two competing models using some precise matrix analytic tools, discuss various statistical properties of the estimators, and analyze the connections among the estimators under the two models.