Open Access
2023 Pretest estimation in combining probability and non-probability samples
Chenyin Gao, Shu Yang
Author Affiliations +
Electron. J. Statist. 17(1): 1492-1546 (2023). DOI: 10.1214/23-EJS2137


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 approach to general parameter estimation by combining gold-standard probability and non-probability samples. We focus on the case when the study variable is observed in both datasets for estimating the target parameters, and each contains other auxiliary variables. Utilizing the probability design, we conduct a pretest procedure to determine the comparability of the non-probability data with the probability data and decide whether or not to leverage the non-probability data in a pooled analysis. When the probability and non-probability data are comparable, our approach combines both data for efficient estimation. Otherwise, we retain only the probability data for estimation. We also characterize the asymptotic distribution of the proposed test-and-pool estimator under a local alternative and provide a data-adaptive procedure to select the critical tuning parameters that target the smallest mean square error of the test-and-pool estimator. Lastly, to deal with the non-regularity of the test-and-pool estimator, we construct a robust confidence interval that has a good finite-sample coverage property.

Funding Statement

Yang’s research is partially supported by the NIH 1R01AG066883 and 1R01ES031651.


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Chenyin Gao. Shu Yang. "Pretest estimation in combining probability and non-probability samples." Electron. J. Statist. 17 (1) 1492 - 1546, 2023.


Received: 1 October 2022; Published: 2023
First available in Project Euclid: 7 June 2023

MathSciNet: MR4598395
zbMATH: 07725162
Digital Object Identifier: 10.1214/23-EJS2137

Primary: 62D05
Secondary: 62E20 , 62F03 , 62F35

Keywords: data integration , dynamic borrowing , non-regularity , Pretest estimator

Vol.17 • No. 1 • 2023
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