Calibration estimation for non-probability samples under two distance functions: a comparative study

Abstract

Calibration estimation is a popular method for making inference from probability samples and dealing with nonresponse problems. Calibration estimation, specially model-assisted calibration estimation, has been extensively explored for inference from non-probability samples in recent years. When there are rich covariates, the variable selection method such as Adaptive LASSO can be used to select important covariates and estimate model parameters for establishing appropriate models in model-assisted calibration estimation. In addition to the established model, distance functions also have an impact on calibration estimation. Different distance functions may produce different calibration estimators. In this paper, traditional calibration estimators, estimated-control model-assisted calibration estimators and estimated-control model-assisted calibration estimators with Adaptive LASSO under the chi-square distance and the modified backward Kullback-Leibler distance are proposed when the population information of covariates is unknown. The calibrated weights based on traditional calibration, model-assisted calibration and model-assisted calibration with Adaptive LASSO under the two distance functions are also derived. Results from a simulation study are presented to compare different calibration estimators. A real data set is also adopted to confirm the performance of the proposed estimators.