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Empirical Bayes Estimation of Small Area Means under a Nested Error Linear Regression Model with Measurement Errors in the Covariates

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  • MAHMOUD TORABI
  • GAURI S. DATTA
  • J. N. K. RAO

Abstract

. Previously, small area estimation under a nested error linear regression model was studied with area level covariates subject to measurement error. However, the information on observed covariates was not used in finding the Bayes predictor of a small area mean. In this paper, we first derive the fully efficient Bayes predictor by utilizing all the available data. We then estimate the regression and variance component parameters in the model to get an empirical Bayes (EB) predictor and show that the EB predictor is asymptotically optimal. In addition, we employ the jackknife method to obtain an estimator of mean squared prediction error (MSPE) of the EB predictor. Finally, we report the results of a simulation study on the performance of our EB predictor and associated jackknife MSPE estimators. Our results show that the proposed EB predictor can lead to significant gain in efficiency over the previously proposed EB predictor.

Suggested Citation

  • Mahmoud Torabi & Gauri S. Datta & J. N. K. Rao, 2009. "Empirical Bayes Estimation of Small Area Means under a Nested Error Linear Regression Model with Measurement Errors in the Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 355-369, June.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:2:p:355-369
    DOI: 10.1111/j.1467-9469.2008.00623.x
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    1. Malay Ghosh & Karabi Sinha & Dalho Kim, 2006. "Empirical and Hierarchical Bayesian Estimation in Finite Population Sampling under Structural Measurement Error Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 591-608, September.
    2. 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.
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    Cited by:

    1. Torabi, Mahmoud, 2012. "Small area estimation using survey weights under a nested error linear regression model with structural measurement error," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 52-60.
    2. Jan Pablo Burgard & María Dolores Esteban & Domingo Morales & Agustín Pérez, 2020. "A Fay–Herriot model when auxiliary variables are measured with error," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 166-195, March.
    3. Marchetti Stefano & Giusti Caterina & Pratesi Monica & Salvati Nicola & Giannotti Fosca & Pedreschi Dino & Rinzivillo Salvatore & Pappalardo Luca & Gabrielli Lorenzo, 2015. "Small Area Model-Based Estimators Using Big Data Sources," Journal of Official Statistics, Sciendo, vol. 31(2), pages 263-281, June.
    4. Jan Pablo Burgard & María Dolores Esteban & Domingo Morales & Agustín Pérez, 2021. "Small area estimation under a measurement error bivariate Fay–Herriot model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 79-108, March.
    5. Datta, Gauri S. & Torabi, Mahmoud & Rao, J.N.K. & Liu, Benmei, 2018. "Small area estimation with multiple covariates measured with errors: A nested error linear regression approach of combining multiple surveys," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 49-59.
    6. 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.
    7. Serena Arima & William R. Bell & Gauri S. Datta & Carolina Franco & Brunero Liseo, 2017. "Multivariate Fay–Herriot Bayesian estimation of small area means under functional measurement error," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1191-1209, October.
    8. Torabi, Mahmoud, 2013. "Likelihood inference in generalized linear mixed measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 549-557.
    9. Priyanka Anjoy, 2023. "Hierarchical Bayes Measurement Error Small Area Model for Estimation of Disaggregated Level Workers Mobility Pattern in India," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(2), pages 339-361, June.
    10. Stefano Marchetti & Caterina Giusti & Nicola Salvati & Monica Pratesi, 2017. "Small area estimation based on M-quantile models in presence of outliers in auxiliary variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 531-555, November.
    11. Jan Pablo Burgard & Joscha Krause & Domingo Morales, 2022. "A measurement error Rao–Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 204-234, March.
    12. J. N. K. Rao, 2015. "Inferential issues in model-based small area estimation: some new developments," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 491-510, December.
    13. Serena Arima & Gauri S. Datta & Brunero Liseo, 2015. "Bayesian Estimators for Small Area Models when Auxiliary Information is Measured with Error," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 518-529, June.
    14. Rao J. N. K., 2015. "Inferential Issues in Model-Based Small Area Estimation: Some New Developments," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 491-510, December.
    15. repec:csb:stintr:v:17:y:2016:i:1:p:9-24 is not listed on IDEAS
    16. Domingo Morales & Joscha Krause & Jan Pablo Burgard, 2022. "On the Use of Aggregate Survey Data for Estimating Regional Major Depressive Disorder Prevalence," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 344-368, March.
    17. J. N. K. Rao, 2015. "Inferential Issues In Model-Based Small Area Estimation: Some New Developments," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 491-510, December.
    18. Erciulescu Andreea L. & Fuller Wayne A., 2016. "Small Area Prediction Under Alternative Model Specifications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 9-24, March.

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