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Abstract:
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Multiple heterogeneous data sources are becoming increasingly available for statistical analyses in the era of big data. As an important example in finite-population inference, we develop a unified framework of the test-and-pool (TAP) approach to general parameter estimation by combining probability (PR) and non-probability (NPR) samples. We focus on the case when the study variable is observed in both PR and NPR data, and each contains other auxiliary variables. Utilizing the probability design, we conduct a pretest procedure to determine the comparability of the NPR data with the PR data and decide whether or not to leverage the NPR data in a pooled analysis. When the PR and NPR data are comparable, our approach combines both data for efficient estimation. Otherwise, we retain only the PR data for estimation. We also characterize the asymptotic distribution of the proposed TAP estimator and provide a data-adaptive procedure to select the critical tuning parameters targeting the smallest mean square error of the TAP estimator. Lastly, to deal with the non-regularity of the TAP estimator, we construct a robust confidence interval that has a good finite-sample coverage property.
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