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Influence functions and robust Bayes and empirical Bayes small area estimation

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  • Malay Ghosh
  • Tapabrata Maiti
  • Ananya Roy

Abstract

We introduce new robust small area estimation procedures based on area-level models. We first find influence functions corresponding to each individual area-level observation by measuring the divergence between the posterior density functions of regression coefficients with and without that observation. Next, based on these influence functions, properly standardized, we propose some new robust Bayes and empirical Bayes small area estimators. The mean squared errors and estimated mean squared errors of these estimators are also found. A small simulation study compares the performance of the robust and the regular empirical Bayes estimators. When the model variance is larger than the sample variance, the proposed robust empirical Bayes estimators are superior. Copyright 2008, Oxford University Press.

Suggested Citation

  • Malay Ghosh & Tapabrata Maiti & Ananya Roy, 2008. "Influence functions and robust Bayes and empirical Bayes small area estimation," Biometrika, Biometrika Trust, vol. 95(3), pages 573-585.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:3:p:573-585
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    File URL: http://hdl.handle.net/10.1093/biomet/asn030
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    Cited by:

    1. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2017. "Transforming response values in small area prediction," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 47-60.
    2. repec:csb:stintr:v:17:y:2016:i:1:p:67-90 is not listed on IDEAS
    3. 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.
    4. Chakraborty Adrijo & Datta Gauri Sankar & Mandal Abhyuday, 2016. "A Two-Component Normal Mixture Alternative to the Fay-Herriot Model," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 67-90, March.
    5. Berg, Emily & Chandra, Hukum, 2014. "Small area prediction for a unit-level lognormal model," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 159-175.
    6. Adrijo Chakraborty & Gauri Sankar Datta & Abhyuday Mandal, 2016. "A Two-Component Normal Mixture Alternative To The Fay-Herriot Model," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 67-90, March.

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