Empirical General Population Assessment of the Variance and Variance Estimators of the Horvitz-Thompson Estimator under Variable Probability Sampling

摘要

The variance and two estimators of variance of the Horvitz-Thompson estimator were studied under randomized, variable probability systematic sampling. Three bivariate distributions, representing the populations, were investigated empirically, with each distribution studied for three correlations of the response variable, y, and auxiliary variable, x. The Horvitz-Thompson and Yates-Grundy variance estimators were compared based on confidence interval coverage, root mean square error, and proportion of negative estimates. The two variance estimators performed equally well except in some high-correlation populations, where the Yates-Grundy estimator had smaller root mean square error, and the Horvitz-Thompson estimator had a few negative estimates. As expected, the gain in precision of variable probability over equal probability sampling was greatest when the correlation between x and y was high, and the gain was reduced or absent when correlations were lower. (Copyright (c) American Statistical Association, 1990.)