  Non-probability sampling is prevailing in survey sampling, but ignoring its
selection bias leads to erroneous inferences. We offer a unified nonparametric
calibration method to estimate the sampling weights for a non-probability
sample by calibrating functions of auxiliary variables in a reproducing kernel
Hilbert space. The consistency and the limiting distribution of the proposed
estimator are established, and the corresponding variance estimator is also
investigated. Compared with existing works, the proposed method is more robust
since no parametric assumption is made for the selection mechanism of the
non-probability sample. Numerical results demonstrate that the proposed method
outperforms its competitors, especially when the model is misspecified. The
proposed method is applied to analyze the average total cholesterol of Korean
citizens based on a non-probability sample from the National Health Insurance
Sharing Service and a reference probability sample from the Korea National
Health and Nutrition Examination Survey.
