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Small area estimation with multiple covariates measured with errors: A nested error linear regression approach of combining multiple surveys

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  • Datta, Gauri S.
  • Torabi, Mahmoud
  • Rao, J.N.K.
  • Liu, Benmei

Abstract

Small area estimation has become a very active area of research in statistics. Many models studied in small area estimation focus on one or more variables of interest from a single survey without paying close attention to the nature of the covariates. It is useful to utilize the idea of borrowing strength from covariates to build a model which combines two (or multiple) surveys. In many real applications, there are also covariates measured with errors. In this paper, we study a nested error linear regression model which has multiple unit- or area-level error-free covariates, possibly coming from administrative records, and multiple area-level covariates subject to structural measurement error where the data on the latter covariates are obtained from multiple surveys. In particular, we derive empirical best predictors of small area means and estimators of mean squared prediction error of the empirical best predictors of small area means. Performance of the proposed approach is studied through a simulation study and also by a real application.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:167:y:2018:i:c:p:49-59
    DOI: 10.1016/j.jmva.2018.04.001
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. Lynn M. R. Ybarra & Sharon L. Lohr, 2008. "Small area estimation when auxiliary information is measured with error," Biometrika, Biometrika Trust, vol. 95(4), pages 919-931.
    5. 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.
    6. 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.
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    Cited by:

    1. Luo, Guowang & Wu, Mixia & Pang, Zhen, 2022. "Estimation of spatial autoregressive models with covariate measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 192(C).

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