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Mean-squared error estimation in transformed Fay-Herriot models


  • Eric V. Slud
  • Tapabrata Maiti


The problem of accurately estimating the mean-squared error of small area estimators within a Fay-Herriot normal error model is studied theoretically in the common setting where the model is fitted to a logarithmically transformed response variable. For bias-corrected empirical best linear unbiased predictor small area point estimators, mean-squared error formulae and estimators are provided, with biases of smaller order than the reciprocal of the number of small areas. The performance of these mean-squared error estimators is illustrated by a simulation study and a real data example relating to the county level estimation of child poverty rates in the US Census Bureau's on-going 'Small area income and poverty estimation' project. Copyright 2006 Royal Statistical Society.

Suggested Citation

  • Eric V. Slud & Tapabrata Maiti, 2006. "Mean-squared error estimation in transformed Fay-Herriot models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 239-257.
  • Handle: RePEc:bla:jorssb:v:68:y:2006:i:2:p:239-257

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    Cited by:

    1. Malay Ghosh & Tatsuya Kubokawa & Yuki Kawakubo, 2014. "Benchmarked Empirical Bayes Methods in Multiplicative Area-level Models with Risk Evaluation," CIRJE F-Series CIRJE-F-918, CIRJE, Faculty of Economics, University of Tokyo.
    2. 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.
    3. Shonosuke Sugasawa & Tatsuya Kubokawa, 2014. "Estimation and Prediction Intervals in Transformed Linear Mixed Models," CIRJE F-Series CIRJE-F-929, CIRJE, Faculty of Economics, University of Tokyo.
    4. repec:exl:29stat:v:16:y:2015:i:4:p:541-562 is not listed on IDEAS
    5. Tatsuya Kubokawa, 2010. "On Measuring Uncertainty of Small Area Estimators with Higher Order Accuracy," CIRJE F-Series CIRJE-F-754, CIRJE, Faculty of Economics, University of Tokyo.
    6. Shonosuke Sugasawa & Tatsuya Kubokawa, 2013. " Parametric Transformed Fay-Herriot Model for Small Area Estimation ," CIRJE F-Series CIRJE-F-911, CIRJE, Faculty of Economics, University of Tokyo.
    7. Molina, Isabel, 2006. "Uncertainty under a multivariate nested-error regression model with logarithmic transformation," DES - Working Papers. Statistics and Econometrics. WS ws066117, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2015. "Parametric transformed Fay–Herriot model for small area estimation," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 295-311.
    9. repec:eee:csdana:v:114:y:2017:i:c:p:47-60 is not listed on IDEAS
    10. repec:bla:jorssa:v:180:y:2017:i:4:p:1057-1088 is not listed on IDEAS
    11. repec:bla:jorssa:v:180:y:2017:i:4:p:1163-1190 is not listed on IDEAS
    12. repec:spr:testjl:v:27:y:2018:i:2:d:10.1007_s11749-017-0551-5 is not listed on IDEAS
    13. Forough Karlberg, 2015. "Small area estimation for skewed data in the presence of zeroes," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 541-562, December.

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