Model-assisted SCAD calibration for non-probability samples

Abstract

Increasing costs and non-response rates of probability samples have provoked the extensive use of non-probability samples. However, non-probability samples are subject to selection bias, resulting in difficulty for inference. Calibration is a popular method to reduce selection bias in non-probability samples. When rich covariate information is available, a key problem is how to select covariates and estimate parameters in calibration for non-probability samples. In this paper, the model-assisted SCAD calibration is proposed to make population inference from non-probability samples. A parametric model between the study variable and covariates is first established. SCAD is then used to estimate the model parameters based on non-probability samples. The modified forward Kullback–Leibler distance is lastly explored to conduct calibration for non-probability samples based on the estimated parametric model. The theoretical properties of the model-assisted SCAD calibration estimator are further derived. Results from simulation studies show that the model-assisted SCAD calibration estimator yields the smallest bias and mean square error compared with other estimators. Also, a real data from the 2017 Netizen Social Awareness Survey (NSAS) is used to demonstrate the proposed methodology.