Minimum MSE regression estimator with estimated population quantities of auxiliary variables

Construction of a regression estimator in which the population means of auxiliary variables are estimated with a larger sample is considered. Using the variances of the estimated population means, and the correlation between auxiliary variables and the variable of interest, a design consistent regression estimator that has minimum model mean squared error under a working model is derived. A limited simulation study shows that the minimum model mean squared error regression estimator performs well compared to the generalized least squares regression estimator, even when the working model is inappropriate.