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Bias‐calibrated estimation from sample surveys containing outliers

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  • A. H. Welsh
  • Elvezio Ronchetti

Abstract

We discuss the problem of estimating finite population parameters on the basis of a sample containing representative outliers. We clarify the motivation for Chambers's bias‐calibrated estimator of the population total and show that bias calibration is a key idea in constructing estimators of finite population parameters. We then link the problem of estimating the population total to distribution function or quantile estimation and explore a methodology based on the use of Chambers's estimator. We also propose methodology based on the use of robust estimates and a bias‐calibrated form of the Chambers and Dunstan estimator of the population distribution function. This proposal leads to a bias‐calibrated estimator of the population total which is an alternative to that of Chambers. We present a small simulation study to illustrate the utility of these estimators.

Suggested Citation

  • A. H. Welsh & Elvezio Ronchetti, 1998. "Bias‐calibrated estimation from sample surveys containing outliers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 413-428.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:2:p:413-428
    DOI: 10.1111/1467-9868.00133
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    Cited by:

    1. Paul A. Smith & Chiara Bocci & Nikos Tzavidis & Sabine Krieg & Marc J. E. Smeets, 2021. "Robust estimation for small domains in business surveys," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 312-334, March.
    2. J. A. Mayor-Gallego & J. L. Moreno-Rebollo & M. D. Jiménez-Gamero, 2019. "Estimation of the finite population distribution function using a global penalized calibration method," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 1-35, March.
    3. G. Bertarelli & R. Chambers & N. Salvati, 2021. "Outlier robust small domain estimation via bias correction and robust bootstrapping," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 331-357, March.

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