The Finite-Population Linear Regression Estimator and Estimators of its Variance—An Empirical Study

The usual variance estimator for the linear regression estimator of a finite population total is examined under some prediction (superpopulation) models. Its bias is compared with that of the least squares variance estimator. Also described are three bias-robust alternatives, one of which is the jackknife variance estimator. The theoretical results are supported by an empirical study in which simple and restricted random samples as well as some purposive (nonrandom) samples are drawn from six real populations. The results illustrate the need for prediction models, and the inadequacy of randomization per se, in providing a theoretical framework for robust inferences.