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A unified approach to robust estimation in finite population sampling

Author

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  • J.-F. Beaumont
  • D. Haziza
  • A. Ruiz-Gazen

Abstract

We argue that the conditional bias associated with a sample unit can be a useful measure of influence in finite population sampling. We use the conditional bias to derive robust estimators that are obtained by downweighting the most influential sample units. Under the model-based approach to inference, our proposed robust estimator is closely related to the well-known estimator of Chambers (1986). Under the design-based approach, it possesses the desirable feature of being applicable with most sampling designs used in practice. For stratified simple random sampling, it is essentially equivalent to the estimator of Kokic & Bell (1994). The proposed robust estimator depends on a tuning constant. In this paper, we propose a method for determining the tuning constant and show that the resulting estimator is consistent. Results from a simulation study suggest that our approach improves the efficiency of standard nonrobust estimators when the population contains units that may be influential if selected in the sample. Copyright 2013, Oxford University Press.

Suggested Citation

  • J.-F. Beaumont & D. Haziza & A. Ruiz-Gazen, 2013. "A unified approach to robust estimation in finite population sampling," Biometrika, Biometrika Trust, vol. 100(3), pages 555-569.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:3:p:555-569
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    File URL: http://hdl.handle.net/10.1093/biomet/ast010
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    Citations

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    Cited by:

    1. Mulry Mary H. & Kaputa Stephen & Thompson Katherine J., 2018. "Setting M-Estimation Parameters for Detection and Treatment of Influential Values," Journal of Official Statistics, Sciendo, vol. 34(2), pages 483-501, June.
    2. Cantoni, Eva & de Luna, Xavier, 2020. "Semiparametric inference with missing data: Robustness to outliers and model misspecification," Econometrics and Statistics, Elsevier, vol. 16(C), pages 108-120.
    3. Martínez-Ovando Juan Carlos & Olivares-Guzmán Sergio I. & Roldán-Rodríguez Adriana, 2014. "Predictive Inference on Finite Populations Segmented in Planned and Unplanned Domains," Working Papers 2014-04, Banco de México.
    4. Valéry Dongmo Jiongo & Pierre Nguimkeu, 2018. "Bootstrapping Mean Squared Errors of Robust Small-Area Estimators: Application to the Method-of-Payments Data," Staff Working Papers 18-28, Bank of Canada.
    5. Valéry Dongmo Jiongo, 2017. "The Bank of Canada 2015 Retailer Survey on the Cost of Payment Methods: Estimation of the Total Private Cost for Large Businesses," Technical Reports 110, Bank of Canada.
    6. Barranco-Chamorro, I. & Jiménez-Gamero, M.D. & Mayor-Gallego, J.A. & Moreno-Rebollo, J.L., 2015. "A case-deletion diagnostic for penalized calibration estimators and BLUP under linear mixed models in survey sampling," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 18-33.
    7. Elena Castilla & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2021. "Robust semiparametric inference for polytomous logistic regression with complex survey design," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(3), pages 701-734, September.
    8. Schmid, Timo & Tzavidis, Nikos & Münnich, Ralf & Chambers, Ray, 2015. "Outlier robust small area estimation under spatial correlation," Discussion Papers 2015/8, Free University Berlin, School of Business & Economics.

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