IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2010cf754.html
   My bibliography  Save this paper

On Measuring Uncertainty of Small Area Estimators with Higher Order Accuracy

Author

Listed:
  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

Abstract

The empirical best linear unbiased predictor (EBLUP) or the empirical Bayes estimator (EB) in the linear mixed model is recognized useful for the small area estimation, because it can increase the estimation precision by using the information from the related areas. Two of the measures of uncertainty of EBLUP is the estimation of the mean squared error (MSE) and the confidence interval, which have been studied under the second-order accuracy in the literature. This paper provides the general analytical results for these two measures in the unified framework, namely, we derive the conditions on the general consistent estimators of the variance components to satisfy the third-order accuracy in the MSE estimation and the confidence interval in the general linear mixed normal models. Those conditions are shown to be satisfied by not only the maximum likelihood (ML) and restricted maximum likelihood (REML), but also the other estimators including the Prasad-Rao and Fay-Herriot estimators in specific models.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:2010cf754
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2010/2010cf754.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gauri Sankar Datta & J. N. K. Rao & David Daniel Smith, 2005. "On measuring the variability of small area estimators under a basic area level model," Biometrika, Biometrika Trust, vol. 92(1), pages 183-196, March.
    2. Cressie, N. & Lahiri, S. N., 1993. "The Asymptotic Distribution of REML Estimators," Journal of Multivariate Analysis, Elsevier, vol. 45(2), pages 217-233, May.
    3. Gauri Sankar Datta & Malay Ghosh & David Daniel Smith & Parthasarathi Lahiri, 2002. "On an Asymptotic Theory of Conditional and Unconditional Coverage Probabilities of Empirical Bayes Confidence Intervals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 139-152, March.
    4. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    5. 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.
    6. Basu, Ruma & Ghosh, J. K. & Mukerjee, Rahul, 2003. "Empirical Bayes prediction intervals in a normal regression model: higher order asymptotics," Statistics & Probability Letters, Elsevier, vol. 63(2), pages 197-203, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Kubokawa, Tatsuya & Nagashima, Bui, 2012. "Parametric bootstrap methods for bias correction in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 1-16.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tatsuya Kubokawa, 2009. "A Review of Linear Mixed Models and Small Area Estimation," CIRJE F-Series CIRJE-F-702, CIRJE, Faculty of Economics, University of Tokyo.
    2. Kubokawa, Tatsuya & Nagashima, Bui, 2012. "Parametric bootstrap methods for bias correction in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 1-16.
    3. Tatsuya Kubokawa, 2009. "Corrected Empirical Bayes Confidence Intervals in Nested Error Regression Models," CIRJE F-Series CIRJE-F-632, CIRJE, Faculty of Economics, University of Tokyo.
    4. Tatsuya Kubokawa & Bui Nagashima, 2011. "Parametric Bootstrap Methods for Bias Correction in Linear Mixed Models," CIRJE F-Series CIRJE-F-801, CIRJE, Faculty of Economics, University of Tokyo.
    5. 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.
    6. 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.
    7. Katarzyna Reluga & María‐José Lombardía & Stefan Sperlich, 2023. "Simultaneous inference for linear mixed model parameters with an application to small area estimation," International Statistical Review, International Statistical Institute, vol. 91(2), pages 193-217, August.
    8. Hirose, Masayo Yoshimori, 2017. "Non-area-specific adjustment factor for second-order efficient empirical Bayes confidence interval," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 67-78.
    9. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2017. "Transforming response values in small area prediction," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 47-60.
    10. 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.
    11. 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.
    12. repec:csb:stintr:v:17:y:2016:i:1:p:9-24 is not listed on IDEAS
    13. Erciulescu Andreea L. & Fuller Wayne A., 2016. "Small Area Prediction Under Alternative Model Specifications," Statistics in Transition New Series, Statistics Poland, vol. 17(1), pages 9-24, March.
    14. Lixia Diao & David D. Smith & Gauri Sankar Datta & Tapabrata Maiti & Jean D. Opsomer, 2014. "Accurate Confidence Interval Estimation of Small Area Parameters Under the Fay–Herriot Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 497-515, June.
    15. 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.
    16. 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.
    17. Malay Ghosh & Tapabrata Maiti, 2008. "Empirical Bayes Confidence Intervals for Means of Natural Exponential Family‐Quadratic Variance Function Distributions with Application to Small Area Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 484-495, September.
    18. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    19. repec:bla:jorssa:v:180:y:2017:i:4:p:1163-1190 is not listed on IDEAS
    20. Torabi, Mahmoud & Rao, J.N.K., 2014. "On small area estimation under a sub-area level model," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 36-55.
    21. 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.
    22. Ralf Münnich & Jan Burgard & Martin Vogt, 2013. "Small Area-Statistik: Methoden und Anwendungen," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 6(3), pages 149-191, March.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tky:fseres:2010cf754. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.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.