Statistica Sinica 24 (2014), 395-414

EFFICIENCY OF MODEL-ASSISTED REGRESSION

ESTIMATORS IN SAMPLE SURVEYS

Jun Shao$^{1,2}$ and Sheng Wang$^3$

$^1$East China Normal University, $^2$University of Wisconsin-Madison

and $^3$Mathematica Policy Research

Abstract: Model-assisted regression estimators are popular in sample surveys for making use of auxiliary information and improving the Horvitz-Thompson estimators of population totals. In the presence of strata and unequal probability sampling, however, there are several ways to form model-assisted regression estimators: regression within each stratum or regression by combining all strata, and a separate ratio adjustment for population size, or a combined ratio adjustment, or no adjustment. In the literature, there is no comprehensive theoretical comparison of these regression estimators. We compare the asymptotic efficiencies of six model-assisted regression estimators under two asymptotic settings. When there are a fixed number of strata with large stratum sample sizes, our result shows that one of the six regression estimators is a clear winner in terms of asymptotic efficiency. When there are a large number of strata with small stratum sample sizes, however, the story is different. Some comparisons in special cases are also made. Some simulation results are presented to examine finite sample performances of regression estimators and their variance estimators.

Key words and phrases: Asymptotic efficiency, bootstrap, combined regression estimators, separate regression estimators, unequal probability without replacement sampling, variance estimation.