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Mean‐squared error estimation in transformed Fay–Herriot models

Author

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  • Eric V. Slud
  • Tapabrata Maiti

Abstract

Summary. 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.

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, April.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:2:p:239-257
    DOI: 10.1111/j.1467-9868.2006.00542.x
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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. Maria Rosaria Ferrante & Silvia Pacei, 2017. "Small domain estimation of business statistics by using multivariate skew normal models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1057-1088, October.
    3. Timo Schmid & Fabian Bruckschen & Nicola Salvati & Till Zbiranski, 2017. "Constructing sociodemographic indicators for national statistical institutes by using mobile phone data: estimating literacy rates in Senegal," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1163-1190, October.
    4. 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.
    5. Shonosuke Sugasawa & Tatsuya Kubokawa & J. N. K. Rao, 2018. "Small area estimation via unmatched sampling and linking 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 407-427, June.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Ghosh Malay, 2020. "Small area estimation: its evolution in five decades," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 1-22, August.
    11. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2020. "Small area estimation of proportions under area-level compositional mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 793-818, September.
    12. Paul Walter & Marcus Groß & Timo Schmid & Nikos Tzavidis, 2021. "Domain prediction with grouped income data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1501-1523, October.
    13. 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.
    14. 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.
    15. Kreutzmann, Ann-Kristin & Marek, Philipp & Salvati, Nicola & Schmid, Timo, 2019. "Estimating regional wealth in Germany: How different are East and West really?," Discussion Papers 35/2019, Deutsche Bundesbank.
    16. Malay Ghosh & Tamal Ghosh & Masayo Y. Hirose, 2022. "Poisson Counts, Square Root Transformation and Small Area Estimation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 449-471, November.
    17. 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.
    18. Karlberg Forough, 2015. "Small Area Estimation for Skewed Data in the Presence of Zeroes," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 541-562, December.
    19. Forough Karlberg, 2015. "Small Area Estimation For Skewed Data In The Presence Of Zeroes," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 541-562, December.
    20. Malay Ghosh, 2020. "Small area estimation: its evolution in five decades," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 1-22, August.

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