Doubly Robust Inference With Nonprobability Survey Samples

Abstract We establish a general framework for statistical inferences with nonprobability survey samples when relevant auxiliary information is available from a probability survey sample. We develop a rigorous procedure for estimating the propensity scores for units in the nonprobability sample, and construct doubly robust estimators for the finite population mean. Variance estimation is discussed under the proposed framework. Results from simulation studies show the robustness and the efficiency of our proposed estimators as compared to existing methods. The proposed method is used to analyze a nonprobability survey sample collected by the Pew Research Center with auxiliary information from the Behavioral Risk Factor Surveillance System and the Current Population Survey. Our results illustrate a general approach to inference with nonprobability samples and highlight the importance and usefulness of auxiliary information from probability survey samples. Supplementary materials for this article are available online.