Asymptotic Variance Estimation and Comparison of Model-Assisted Regression Estimators in Sample Surveys

• Activity Number: 122
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Survey Research Methods
• Author(s): Jun Shao and Sheng Wang*+
• Companies: University of Wisconsin-Madison and Mathematica Policy Research
• Keywords: Variance estimation ; bootstrap ; combined regression estimators ; separate regression estimators ; asymptotic efficiency ; unequal probability without replacement sampling

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, i.e., 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 our paper, the asymptotic normalities of the estimators are established under two different asymptotic settings. In both cases, we consider variance estimation by applying substitution or the bootstrap, which is useful in large sample inference. The relative efficiencies among these six estimators are obtained based on the asymptotic properties under two settings. Some simulation results are presented to examine finite sample performances of regression estimators and their variance estimators.