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Doubly Robust Inference With Nonprobability Survey Samples

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  • Yilin Chen
  • Pengfei Li
  • Changbao Wu

Abstract

We establish a general framework for statistical inferences with nonprobability survey samples when relevant auxiliary information is available from a probability survey sample. We develop a rigorous procedure for estimating the propensity scores for units in the nonprobability sample, and construct doubly robust estimators for the finite population mean. Variance estimation is discussed under the proposed framework. Results from simulation studies show the robustness and the efficiency of our proposed estimators as compared to existing methods. The proposed method is used to analyze a nonprobability survey sample collected by the Pew Research Center with auxiliary information from the Behavioral Risk Factor Surveillance System and the Current Population Survey. Our results illustrate a general approach to inference with nonprobability samples and highlight the importance and usefulness of auxiliary information from probability survey samples. Supplementary materials for this article are available online.

Suggested Citation

  • Yilin Chen & Pengfei Li & Changbao Wu, 2020. "Doubly Robust Inference With Nonprobability Survey Samples," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 2011-2021, December.
    • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:532:p:2011-2021
    DOI: 10.1080/01621459.2019.1677241
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    Cited by:

    1. Ray Chambers & Setareh Ranjbar & Nicola Salvati & Barbara Pacini, 2022. "Weighting, informativeness and causal inference, with an application to rainfall enhancement," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1584-1612, October.
    2. Ramón Ferri-García & María del Mar Rueda & Andrés Cabrera-León, 2021. "Self-Perceived Health, Life Satisfaction and Related Factors among Healthcare Professionals and the General Population: Analysis of an Online Survey, with Propensity Score Adjustment," Mathematics, MDPI, vol. 9(7), pages 1-27, April.
    3. Ieva Burakauskaitė & Andrius Čiginas, 2023. "An Approach to Integrating a Non-Probability Sample in the Population Census," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    4. Li, Wei & Luo, Shanshan & Xu, Wangli, 2024. "Calibrated regression estimation using empirical likelihood under data fusion," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    5. Sixia Chen & Alexandra May Woodruff & Janis Campbell & Sara Vesely & Zheng Xu & Cuyler Snider, 2023. "Combining Probability and Nonprobability Samples by Using Multivariate Mass Imputation Approaches with Application to Biomedical Research," Stats, MDPI, vol. 6(2), pages 1-9, May.
    6. Bing Li & Constantine Gatsonis & Issa J. Dahabreh & Jon A. Steingrimsson, 2023. "Estimating the area under the ROC curve when transporting a prediction model to a target population," Biometrics, The International Biometric Society, vol. 79(3), pages 2382-2393, September.
    7. Chien-Min Huang & F. Jay Breidt, 2023. "A dual-frame approach for estimation with respondent-driven samples," METRON, Springer;Sapienza Università di Roma, vol. 81(1), pages 65-81, April.
    8. Xinyu Li & Wang Miao & Fang Lu & Xiao‐Hua Zhou, 2023. "Improving efficiency of inference in clinical trials with external control data," Biometrics, The International Biometric Society, vol. 79(1), pages 394-403, March.
    9. Ramón Ferri-García & Jean-François Beaumont & Keven Bosa & Joanne Charlebois & Kenneth Chu, 2022. "Weight smoothing for nonprobability surveys," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 619-643, September.
    10. Xiaojun Mao & Zhonglei Wang & Shu Yang, 2023. "Matrix completion under complex survey sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(3), pages 463-492, June.
    11. Luis Castro-Martín & María del Mar Rueda & Ramón Ferri-García & César Hernando-Tamayo, 2021. "On the Use of Gradient Boosting Methods to Improve the Estimation with Data Obtained with Self-Selection Procedures," Mathematics, MDPI, vol. 9(23), pages 1-23, November.

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