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Empirical bootstrap bias correction and estimation of prediction mean square error in small area estimation

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  • D. Pfeffermann
  • S. Correa

Abstract

We develop a method for bias correction, which models the error of the target estimator as a function of the corresponding estimator obtained from bootstrap samples, and the original estimators and bootstrap estimators of the parameters governing the model fitted to the sample data. This is achieved by considering a number of plausible parameter values, generating a pseudo original sample for each parameter and bootstrap samples for each such sample, and then searching for an appropriate functional relationship. Under certain conditions, the procedure also permits estimation of the mean square error of the bias corrected estimator. The method is applied for estimating the prediction mean square error in small area estimation of proportions under a generalized mixed model. Empirical comparisons with jackknife and bootstrap methods are presented. Copyright 2012, Oxford University Press.

Suggested Citation

  • D. Pfeffermann & S. Correa, 2012. "Empirical bootstrap bias correction and estimation of prediction mean square error in small area estimation," Biometrika, Biometrika Trust, vol. 99(2), pages 457-472.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:2:p:457-472
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    File URL: http://hdl.handle.net/10.1093/biomet/ass010
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    Cited by:

    1. Andreea L. Erciulescu & Wayne A. Fuller, 2016. "Small Area Prediction Under Alternative Model Specifications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 9-24, March.
    2. Tomáš Hobza & Domingo Morales & Laureano Santamaría, 2018. "Small area estimation of poverty proportions under unit-level temporal binomial-logit mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 270-294, June.
    3. J. N. K. Rao, 2015. "Inferential issues in model-based small area estimation: some new developments," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 491-510, December.
    4. repec:csb:stintr:v:17:y:2016:i:1:p:9-24 is not listed on IDEAS
    5. Erciulescu Andreea L. & Fuller Wayne A., 2016. "Small Area Prediction Under Alternative Model Specifications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 9-24, March.
    6. Tzavidis, Nikos & Zhang, Li-Chun & Luna Hernandez, Angela & Schmid, Timo & Rojas-Perilla, Natalia, 2016. "From start to finish: A framework for the production of small area official statistics," Discussion Papers 2016/13, Free University Berlin, School of Business & Economics.
    7. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.
    8. Rao J. N. K., 2015. "Inferential Issues in Model-Based Small Area Estimation: Some New Developments," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 491-510, December.
    9. Huapeng Li & Yukun Liu & Riquan Zhang, 2019. "Small area estimation under transformed nested-error regression models," Statistical Papers, Springer, vol. 60(4), pages 1397-1418, August.
    10. J. N. K. Rao, 2015. "Inferential Issues In Model-Based Small Area Estimation: Some New Developments," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 491-510, December.

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