Estimation of variance of the regression estimator


The regression estimator and the ratio estimator are commonly used in survey practice. In the past more attention has been given to the ratio estimator because of its computational ease and applicability for general sampling designs. The ratio estimator is appropriate for populations whose regression line passes close to the origin. If the intercept of the regression line is significantly nonzero, however, it is much less efficient than the regression estimator (Deng 1984). In general, apart from n–2terms, the mean squared error (MSE) of the former is bigger than that of the latter (Cochran 1977, p. 196). Given the present computing capacity, the computational advantage of the ratio estimator should be less of a concern and the regression estimator will gain wider popularity. The main purpose of this article is to provide a theoretical and empirical comparison of several variance estimators for the regression estimator in simple random sampling without replacement. The companion problem for the ratio estimator has been studied in the literature (see Wu and Deng 1983). Under comparison are several design-based and model-based estimators and a new class of estimators. Their second-order expressions and biases are derived and compared. Empirical results on the biases and MSE’s of the variance estimators and the conditional and unconditional coverage probabilities of their associated t intervals are obtained. They lend support to the theoretical results and suggest questions for further investigation. Our empirical and theoretical study provides a guide to the use of these estimators in practice. © 1976 Taylor & Francis Group, LLC.

Publication Title

Journal of the American Statistical Association