Doubly robust estimation with graphical structure among predictors for integrating probability and non-probability samples

Non-probability samples such as web survey data are widely used in different fields because of their low cost, short period and high efficiency. However, it is difficult to infer the population due to the absence of inclusion probabilities of non-probability samples. The propensity score approach, superpopulation model approach and doubly robust approach have been used for inference with non-probability samples. However, when there is a relatively rich set of covariates or predictors, variable selection and correlations between predictors become important in modeling. In this paper, doubly robust estimation methods are proposed via incorporating a penalty and double penalty graphical structures among predictors for non-probability samples with high-dimensional data. Specifically, not only are graphical structures among predictors considered to describe the relationships between covariates in superpopulation modeling, but the inverse of the estimated inclusion probabilities of non-probability samples are also added to the objective function for estimating superpopulation parameters in the proposed methods. The asymptotic properties of the proposed estimators and variance estimation are discussed. Simulation studies are further conducted to verify the performance of the proposed methods. Lastly, the proposed methods are adopted to analyze a Rattus norvegicus eye eQTL experiment data set.