IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v68y2006i2p239-257.html
   My bibliography  Save this article

Mean‐squared error estimation in transformed Fay–Herriot models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9868.2006.00542.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9868.2006.00542.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. repec:bla:jorssa:v:180:y:2017:i:4:p:1163-1190 is not listed on IDEAS
    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, Statistics Poland, 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, Statistics Poland, 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssb:v:68:y:2006:i:2:p:239-257. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.