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Constrained Bayes estimation in small area models with functional measurement error

Author

Listed:
  • Elaheh Torkashvand

    (University of Manitoba)

  • Mohammad Jafari Jozani

    (University of Manitoba)

  • Mahmoud Torabi

    (University of Manitoba)

Abstract

In survey sampling, policy decisions regarding allocation of resources to subgroups, called small areas, or determination of subgroups with specific properties in a population are based on reliable estimates of small area parameters. However, the information is often collected at a different scale than these subgroups. Hence, we need to estimate characteristics of subgroups based on the coarser scale data. One of the main interests in small area estimation is to produce an ensemble of small area parameters whose distribution across small areas is close to the corresponding distribution of true parameters. In this paper, we consider the unit-level nested error linear regression model which is commonly used in small area estimation. We study the case where the covariate in the model is assumed to have measurement error. To study this complex model, we propose to use constrained Bayes method to estimate the true covariate to build the small area Bayes predictor. We also provide some measures of performance such as sensitivity, specificity, and positive/negative predictive values for the constructed Bayes predictor. We estimate the model parameters using the method of moments and Bayesian approach to get corresponding empirical and hierarchical Bayes predictors. The performance of our proposed approach is evaluated through a simulation study and a real data application.

Suggested Citation

  • Elaheh Torkashvand & Mohammad Jafari Jozani & Mahmoud Torabi, 2016. "Constrained Bayes estimation in small area models with functional measurement error," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 710-730, December.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:4:d:10.1007_s11749-016-0492-4
    DOI: 10.1007/s11749-016-0492-4
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    References listed on IDEAS

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    1. 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.
    2. G. Datta & M. Ghosh & R. Steorts & J. Maples, 2011. "Bayesian benchmarking with applications to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 574-588, November.
    3. Neung Ha & Partha Lahiri, 2014. "Comments on: Single and two-stage cross-sectional and time series benchmarking procedures for small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 670-673, December.
    4. Danny Pfeffermann & Anna Sikov & Richard Tiller, 2014. "Single- and two-stage cross-sectional and time series benchmarking procedures for small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 631-666, December.
    5. 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.
    6. 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;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 558-579, November.
    7. Danny Pfeffermann & Anna Sikov & Richard Tiller, 2014. "Rejoinder on: Single- and two-stage cross-sectional and time series benchmarking procedures for small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 686-690, December.
    8. 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;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 342-364, August.
    9. Malay Ghosh & Rebecca Steorts, 2013. "Two-stage benchmarking as applied to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 670-687, November.
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