Doubly Robust Estimation of a Population Mean from a Non-probability Sample

Doubly robust estimators have long been advocated in the literature on missing data and causal inference. Recently, their use has also been proposed for inference in non-probability sampling. As in the missing data setting, non-probability sampling introduces a selection bias problem. Consequently, making valid inferences requires the use of auxil-iary variables and modeling their influence on either the outcome variable or the selection mechanism. A doubly robust estimator requires speci-fying both a model for the selection mechanism and a model for the outcome variable, ensuring consistency if either model is correctly spec-ified. This study aims to analyze how the performance of certain doubly robust estimators is affected when the selection mechanism is misspeci-fied, particularly when it generates extreme and highly variable weights. The findings emphasize the importance of evaluating the empirical distri-bution of estimated weights, even when using a doubly robust estimator.