Functional Calibration under Non-Probability Survey Sampling

TL;DR

This paper introduces a robust nonparametric calibration method for estimating sampling weights in non-probability surveys, improving inference accuracy without relying on parametric assumptions.

Contribution

It proposes a unified kernel-based calibration approach that is more robust and performs better under model misspecification compared to existing methods.

Findings

The method achieves consistent estimation and known limiting distribution.

It outperforms competitors in numerical simulations, especially under model misspecification.

Applied to Korean cholesterol data, it provided reliable estimates from non-probability samples.

Abstract

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.