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Estimation and Prediction Intervals in Transformed Linear Mixed Models

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  • Shonosuke Sugasawa

    (Graduate School of Economics, The University of Tokyo)

  • Tatsuya Kubokawa

    (Faculty of Economics, The University of Tokyo)

Abstract

   For analyzing positive or bounded data, this paper suggests parametrically transformed nested error regression models (TNERM), which not only include the log-transformed model, but also adjust flexibly the transformation parameter to fit the data to a normal linear regression. Conditions on the transformation are derived for consistency of the maximum likelihood estimator for the transformation parameter. The conditions are satisfied by the dual power transformation for positive data and the dual power logistic transformation for bounded data. In order to calibrate uncertainty of the transformed empirical best linear unbiased predictor (TEBLUP), the paper derives prediction intervals with second-order accuracy based on the parametric bootstrap method. Conditional prediction intervals given data in the area of interest are also constructed. The proposed methods are investigated through simulation and empirical studies.

Suggested Citation

  • 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.
  • Handle: RePEc:tky:fseres:2014cf929
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    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. Yang, Zhenlin, 2006. "A modified family of power transformations," Economics Letters, Elsevier, vol. 92(1), pages 14-19, July.
    3. 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.
    4. Gauri Datta & Tatsuya Kubokawa & Isabel Molina & J. Rao, 2011. "Estimation of mean squared error of model-based small area estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 367-388, August.
    5. 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.
    6. 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.
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