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Empirical best prediction of small area bivariate parameters

Author

Listed:
  • María Dolores Esteban
  • María José Lombardía
  • Esther López‐Vizcaíno
  • Domingo Morales
  • Agustín Pérez

Abstract

This paper introduces empirical best predictors of small area bivariate parameters, like ratios of sums or sums of ratios, by assuming that the target unit‐level vector follows a bivariate nested error regression model. The corresponding means squared errors are estimated by parametric bootstrap. Several simulation experiments empirically study the behavior of the introduced statistical methodology. An application to real data from the Spanish household budget survey gives estimators of ratios of food household expenditures by provinces.

Suggested Citation

  • María Dolores Esteban & María José Lombardía & Esther López‐Vizcaíno & Domingo Morales & Agustín Pérez, 2022. "Empirical best prediction of small area bivariate parameters," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1699-1727, December.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:4:p:1699-1727
    DOI: 10.1111/sjos.12618
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    References listed on IDEAS

    as
    1. Monique Graf & J. Miguel Marín & Isabel Molina, 2019. "A generalized mixed model for skewed distributions 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. 28(2), pages 565-597, June.
    2. María Guadarrama & Isabel Molina & J. N. K. Rao, 2016. "A Comparison Of Small Area Estimation Methods For Poverty Mapping," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 41-66, March.
    3. Yolanda Marhuenda & Isabel Molina & Domingo Morales & J. N. K. Rao, 2017. "Poverty mapping in small areas under a twofold nested error regression model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1111-1136, October.
    4. Gonzalez-Manteiga, W. & Lombardia, M.J. & Molina, I. & Morales, D. & Santamaria, L., 2007. "Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2720-2733, February.
    5. Esther López-Vizcaíno & María José Lombardía & Domingo Morales, 2015. "Small area estimation of labour force indicators under a multinomial model with correlated time and area effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 535-565, June.
    6. repec:csb:stintr:v:17:y:2016:i:1:p:9-24 is not listed on IDEAS
    7. repec:csb:stintr:v:17:y:2016:i:1:p:41-66 is not listed on IDEAS
    8. J. L. Scealy & A. H. Welsh, 2017. "A Directional Mixed Effects Model for Compositional Expenditure Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 24-36, January.
    9. Roberto Benavent & Domingo Morales, 2021. "Small area estimation under a temporal bivariate area-level linear mixed model with independent time effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 195-222, March.
    10. Azka Ubaidillah & Khairil Anwar Notodiputro & Anang Kurnia & I. Wayan Mangku, 2019. "Multivariate Fay-Herriot models for small area estimation with application to household consumption per capita expenditure in Indonesia," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(15), pages 2845-2861, November.
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    12. Isabel Molina & Ayoub Saei & M. José Lombardía, 2007. "Small area estimates of labour force participation under a multinomial logit mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 975-1000, October.
    13. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2022. "Small area estimation of expenditure means and ratios under a unit-level bivariate linear mixed model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(1), pages 143-168, January.
    14. Stefano Marchetti & Luca Secondi, 2017. "Estimates of Household Consumption Expenditure at Provincial Level in Italy by Using Small Area Estimation Methods: “Real” Comparisons Using Purchasing Power Parities," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 131(1), pages 215-234, March.
    15. 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.
    16. Innocent Ngaruye & Joseph Nzabanita & Dietrich von Rosen & Martin Singull, 2017. "Small area estimation under a multivariate linear model for repeated measures data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(21), pages 10835-10850, November.
    17. Boubeta, Miguel & Lombardía, María José & Morales, Domingo, 2017. "Poisson mixed models for studying the poverty in small areas," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 32-47.
    18. Jiming Jiang & P. Lahiri, 2001. "Empirical Best Prediction for Small Area Inference with Binary Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 217-243, June.
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