Superpopulation model inference for non probability samples under informative sampling with high-dimensional data

Non probability samples have been widely used in various fields. However, non probability samples suffer from selection biases due to the unknown selection probabilities. Superpopulation model inference methods have been discussed to solve this problem, but these approaches require the non informative sampling assumption. When the sampling mechanism is informative sampling, that is, selection probabilities are related to the outcome variable, the previous inference methods may be invalid. Moreover, we may encounter a large number of covariates in practice, which poses a new challenge for inference from non probability samples under informative sampling. In this article, the superpopulation model approaches under informative sampling with high-dimensional data are developed to perform valid inferences from non probability samples. Specifically, a semiparametric exponential tilting model is established to estimate selection probabilities, and the sample distribution is derived for estimating the superpopulation model parameters. Moreover, SCAD, adaptive LASSO, and Model-X knockoffs are employed to select variables, and estimate parameters in superpopulation modeling. Asymptotic properties of the proposed estimators are established. Results from simulation studies are presented to compare the performance of the proposed estimators with the naive estimator, which ignores informative sampling. The proposed methods are further applied to the National Health and Nutrition Examination Survey data.