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QR prediction for statistical data integration

Author

Listed:
  • Estelle Medous

    (TSE-R - TSE-R Toulouse School of Economics – Recherche - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Camelia Goga

    (UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Anne Ruiz-Gazen

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Jean-François Beaumont
  • Alain Dessertaine
  • Pauline Puech

    (Groupe La Poste)

Abstract

In this paper, we investigate how a big non-probability database can be used to improve estimates of finite population totals from a small probability sample through data integration techniques. In the situation where the study variable is observed in both data sources, Kim and Tam (2021) proposed two design-consistent estimators that can be justified through dual frame survey theory. First, we provide conditions ensuring that these estimators are more efficient than the Horvitz-Thompson estimator when the probability sample is selected using either Poisson sampling or simple random sampling without replacement. Then, we study the class of QR predictors, introduced by Särndal and Wright (1984), to handle the less common case where the non-probability database contains no study variable but auxiliary variables. We also require that the non-probability database is large and can be linked to the probability sample. We provide conditions ensuring that the QR predictor is asymptotically design-unbiased. We derive its asymptotic design variance and provide a consistent design-based variance estimator. We compare the design properties of different predictors, in the class of QR predictors, through a simulation study. This class includes a model-based predictor, a model-assisted estimator and a cosmetic estimator. In our simulation setups, the cosmetic estimator performed slightly better than the model-assisted estimator. These findings are confirmed by an application to La Poste data, which also illustrates that the properties of the cosmetic estimator are preserved irrespective of the observed non-probability sample.

Suggested Citation

  • Estelle Medous & Camelia Goga & Anne Ruiz-Gazen & Jean-François Beaumont & Alain Dessertaine & Pauline Puech, 2023. "QR prediction for statistical data integration," Post-Print hal-04390127, HAL.
    • Handle: RePEc:hal:journl:hal-04390127
    as

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    References listed on IDEAS

    as
    1. J. N. K. Rao, 2021. "On Making Valid Inferences by Integrating Data from Surveys and Other Sources," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 242-272, May.
    2. Jae‐Kwang Kim & Siu‐Ming Tam, 2021. "Data Integration by Combining Big Data and Survey Sample Data for Finite Population Inference," International Statistical Review, International Statistical Institute, vol. 89(2), pages 382-401, August.
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