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On parametric bootstrap methods for small area prediction

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  • Peter Hall
  • Tapabrata Maiti
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    Abstract

    The particularly wide range of applications of small area prediction, e.g. in policy making decisions, has meant that this topic has received substantial attention in recent years. The problems of estimating mean-squared predictive error, of correcting that estimator for bias and of constructing prediction intervals have been addressed by various workers, although existing methodology is still restricted to a narrow range of models. To overcome this difficulty we develop new, bootstrap-based methods, which are applicable in very general settings, for constructing bias-corrected estimators of mean-squared error and for computing prediction regions. Unlike existing techniques, which are based largely on Taylor expansions, our bias-corrected mean-squared error estimators do not require analytical calculation. They also have the property that they are non-negative. Our prediction intervals have a high degree of coverage accuracy, "O"("n"-super- - 3), where "n" is the number of areas, if double-bootstrap methods are employed. The techniques do not depend on the form of the small area estimator and are applicable to general two-level, small area models, where the variables at either level can be discrete or continuous and, in particular, can be non-normal. Most importantly, the new methods are simple and easy to apply. Copyright 2006 Royal Statistical Society.

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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society Series B.

    Volume (Year): 68 (2006)
    Issue (Month): 2 ()
    Pages: 221-238

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    Handle: RePEc:bla:jorssb:v:68:y:2006:i:2:p:221-238

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    Cited by:
    1. 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.
    2. Isabel Molina & Nicola Salvati & Monica Pratesi, 2009. "Bootstrap for estimating the MSE of the Spatial EBLUP," Computational Statistics, Springer, vol. 24(3), pages 441-458, August.
    3. M. Ugarte & A. Militino & T. Goicoa, 2009. "Benchmarked estimates in small areas using linear mixed models with restrictions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 18(2), pages 342-364, August.
    4. 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.
    5. 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.
    6. Ralf Münnich & Jan Burgard & Martin Vogt, 2013. "Small Area-Statistik: Methoden und Anwendungen," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer, vol. 6(3), pages 149-191, March.
    7. 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.
    8. Arnab Bhattacharjee & Eduardo Castro & Taps Maiti & João Marques, 2014. "Endogenous spatial structure and delineation of submarkets: A new framework with application to housing markets," SEEC Discussion Papers 1403, Spatial Economics and Econometrics Centre, Heriot Watt University.
    9. Isabel Molina & J.N.K. Rao, 2009. "Small area estimation on poverty indicators," Statistics and Econometrics Working Papers ws091505, Universidad Carlos III, Departamento de Estadística y Econometría.
    10. LONGFORD Nicholas Tibor, 2011. "Policy-related small.area estimation," CEPS/INSTEAD Working Paper Series 2011-44, CEPS/INSTEAD.
    11. 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.
    12. Cristina Rueda & José Menéndez & Federico Gómez, 2010. "Small area estimators based on restricted mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 19(3), pages 558-579, November.
    13. Timo Schmid & Ralf Münnich, 2014. "Spatial robust small area estimation," Statistical Papers, Springer, vol. 55(3), pages 653-670, August.
    14. González-Manteiga, W. & Lombardi­a, M.J. & Molina, I. & Morales, D. & Santamari­a, L., 2008. "Analytic and bootstrap approximations of prediction errors under a multivariate Fay-Herriot model," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5242-5252, August.

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