[show abstract][hide abstract] ABSTRACT: 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.
[show abstract][hide abstract] ABSTRACT: A procedure for constructing a vector of regression weights is considered. Under the re-gression superpopulation model, the ridge regression estimator that has minimum model mean squared error is derived. Through a simulation study, the ridge regression weights, regression weights, quadratic programming weights and raking ratio weights are compared. The ridge regression procedure with weights bounded by zero performed very well.
[show abstract][hide abstract] ABSTRACT: Estimation of the population mean under the regression model with random components is considered. Conditions under which the random components regression estimator is design consistent are given. It is shown that consistency holds when incorrect values are used for the variance components. The regression estimator constructed with model parameters that differ considerably from the true parameters performed well in a Monte Carlo study. Variance estimators for the regression predictor are suggested. A variance estimator appropriate for estimators constructed with a biased estimator for the between-group variance component performed well in the Monte Carlo study.