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Multivariate Fay–Herriot models for small area estimation

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  • Benavent, Roberto
  • Morales, Domingo

Abstract

Multivariate Fay–Herriot models for estimating small area indicators are introduced. Among the available procedures for fitting linear mixed models, the residual maximum likelihood (REML) is employed. The empirical best predictor (EBLUP) of the vector of area means is derived. An approximation to the matrix of mean squared crossed prediction errors (MSE) is given and four MSE estimators are proposed. The first MSE estimator is a plug-in version of the MSE approximation. The remaining MSE estimators combine parametric bootstrap with the analytic terms of the MSE approximation. Several simulation experiments are performed in order to assess the behavior of the multivariate EBLUP and for comparing the MSE estimators. The developed methodology and software are applied to data from the 2005 and 2006 Spanish living condition surveys. The target of the application is the estimation of poverty proportions and gaps at province level.

Suggested Citation

  • Benavent, Roberto & Morales, Domingo, 2016. "Multivariate Fay–Herriot models for small area estimation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 372-390.
    • Handle: RePEc:eee:csdana:v:94:y:2016:i:c:p:372-390
    DOI: 10.1016/j.csda.2015.07.013
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    References listed on IDEAS

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    1. Marhuenda, Yolanda & Molina, Isabel & Morales, Domingo, 2013. "Small area estimation with spatio-temporal Fay–Herriot models," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 308-325.
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    6. 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.
    7. W. R. Bell & G. S. Datta & M. Ghosh, 2013. "Benchmarking small area estimators," Biometrika, Biometrika Trust, vol. 100(1), pages 189-202.
    8. 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.
    9. 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.
    10. Esteban, M.D. & Morales, D. & Pérez, A. & Santamaría, L., 2012. "Small area estimation of poverty proportions under area-level time models," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2840-2855.
    11. 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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    Cited by:

    1. 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.
    2. Saurav Guha & Hukum Chandra, 2022. "Multivariate Small Area Modelling for Measuring Micro Level Earning Inequality: Evidence from Periodic Labour Force Survey of India," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 162(2), pages 643-663, July.
    3. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2017. "Transforming response values in small area prediction," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 47-60.
    4. Yegnanew A. Shiferaw, 2023. "Mapping Disaggregate-Level Agricultural Households in South Africa Using a Hierarchical Bayes Small Area Estimation Approach," Agriculture, MDPI, vol. 13(3), pages 1-17, March.
    5. Bilton, Penny & Jones, Geoff & Ganesh, Siva & Haslett, Steve, 2017. "Classification trees for poverty mapping," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 53-66.
    6. Saurav Guha & Hukum Chandra, 2021. "Measuring and Mapping Disaggregate Level Disparities in Food Consumption and Nutritional Status via Multivariate Small Area Modelling," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 154(2), pages 623-646, April.
    7. Armalia Desiyanti & Irlandia Ginanjar & Toni Toharudin, 2022. "Application of an Empirical Best Linear Unbiased Prediction Fay–Herriot (EBLUP-FH) Multivariate Method with Cluster Information to Estimate Average Household Expenditure," Mathematics, MDPI, vol. 11(1), pages 1-25, December.
    8. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2023. "Small area estimation of average compositions under multivariate nested error regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 651-676, June.
    9. Angelo Moretti, 2023. "Estimation of small area proportions under a bivariate logistic mixed model," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3663-3684, August.

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