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Prediction Error of Small Area Predictors Shrinking Both Means and Variances

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  • Tapabrata Maiti
  • Hao Ren
  • Samiran Sinha

Abstract

type="main" xml:id="sjos12061-abs-0001"> The article considers a new approach for small area estimation based on a joint modelling of mean and variances. Model parameters are estimated via expectation–maximization algorithm. The conditional mean squared error is used to evaluate the prediction error. Analytical expressions are obtained for the conditional mean squared error and its estimator. Our approximations are second-order correct, an unwritten standardization in the small area literature. Simulation studies indicate that the proposed method outperforms the existing methods in terms of prediction errors and their estimated values.

Suggested Citation

  • Tapabrata Maiti & Hao Ren & Samiran Sinha, 2014. "Prediction Error of Small Area Predictors Shrinking Both Means and Variances," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 775-790, September.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:3:p:775-790
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    File URL: http://hdl.handle.net/10.1111/sjos.12061
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    References listed on IDEAS

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    1. Sharon L. Lohr & J. N. K. Rao, 2009. "Jackknife estimation of mean squared error of small area predictors in nonlinear mixed models," Biometrika, Biometrika Trust, vol. 96(2), pages 457-468.
    2. Wang, Junyuan & Fuller, Wayne A., 2003. "The Mean Squared Error of Small Area Predictors Constructed With Estimated Area Variances," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 716-723, January.
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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. Shonosuke Sugasawa & Hiromasa Tamae & Tatsuya Kubokawa, 2017. "Bayesian Estimators for Small Area Models Shrinking Both Means and Variances," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 150-167, March.
    3. Lu Chen & Luca Sartore & Habtamu Benecha & Valbona Bejleri & Balgobin Nandram, 2022. "Smoothing County-Level Sampling Variances to Improve Small Area Models’ Outputs," Stats, MDPI, vol. 5(3), pages 1-18, September.
    4. Joscha Krause & Jan Pablo Burgard & Domingo Morales, 2022. "Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 65-96, February.
    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. Gershunskaya Julie, 2020. "Discussion of “Small area estimation: its evolution in five decades”, by Malay Ghosh," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 23-29, August.
    7. Xin Wang & Emily Berg & Zhengyuan Zhu & Dongchu Sun & Gabriel Demuth, 2018. "Small Area Estimation of Proportions with Constraint for National Resources Inventory Survey," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(4), pages 509-528, December.
    8. Shonosuke Sugasawa & Tatsuya Kubokawa, 2015. "Heteroscedastic Nested Error Regression Models with Variance Functions," CIRJE F-Series CIRJE-F-978, CIRJE, Faculty of Economics, University of Tokyo.
    9. Julie Gershunskaya, 2020. "Discussion of "Small area estimation: its evolution in five decades", by Malay Ghosh," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 23-29, August.
    10. Hiromasa Tamae & Tatsuya Kubokawa, 2015. "Small Area Predictors with Dual Shrinkage of Means and Variances," CIRJE F-Series CIRJE-F-982, CIRJE, Faculty of Economics, University of Tokyo.
    11. Peter A. Gao & Jonathan Wakefield, 2023. "A Spatial Variance‐Smoothing Area Level Model for Small Area Estimation of Demographic Rates," International Statistical Review, International Statistical Institute, vol. 91(3), pages 493-510, December.

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