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Non-parametric bootstrap mean squared error estimation for M-quantile estimators of small area averages, quantiles and poverty indicators

Author

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  • Marchetti, Stefano
  • Tzavidis, Nikos
  • Pratesi, Monica

Abstract

Small area estimation is conventionally concerned with the estimation of small area averages and totals. More recently emphasis has been also placed on the estimation of poverty indicators and of key quantiles of the small area distribution function using robust models, for example, the M-quantile small area model. In parallel to point estimation, Mean Squared Error (MSE) estimation is an equally crucial and challenging task. However, while analytic MSE estimation for small area averages is possible, analytic MSE estimation for quantiles and poverty indicators is difficult. Moreover, one of the main criticisms of the analytic MSE estimator for M-quantile estimates of small area averages is that it can be unstable when the area-specific sample sizes are small. A non-parametric bootstrap framework for MSE estimation for small area averages, quantiles and poverty indicators estimated with the M-quantile small area model is proposed. Emphasis is placed on second order properties of MSE estimators with results suggesting that the bootstrap MSE estimator is more stable than corresponding analytic MSE estimators. The proposed bootstrap is evaluated in a series of simulation studies under different parametric assumptions for the model error terms and different scenarios for the area-specific sample and population sizes. Finally, results from the application of the proposed MSE estimator to real income data from the European Survey of Income and Living Conditions (EU-SILC) in Italy are presented and information on the availability of R functions that can be used for implementing the proposed estimation procedures in practice is provided.

Suggested Citation

  • Marchetti, Stefano & Tzavidis, Nikos & Pratesi, Monica, 2012. "Non-parametric bootstrap mean squared error estimation for M-quantile estimators of small area averages, quantiles and poverty indicators," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2889-2902.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:10:p:2889-2902
    DOI: 10.1016/j.csda.2012.01.023
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    References listed on IDEAS

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    1. 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.
    2. Hongjian Yu & Yueyan Wang & Jean Opsomer & Pan Wang & Ninez A. Ponce, 2018. "A design‐based approach to small area estimation using a semiparametric generalized linear mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1151-1167, October.
    3. Domingo Morales & María del Mar Rueda & Dolores Esteban, 2018. "Model-Assisted Estimation of Small Area Poverty Measures: An Application within the Valencia Region in Spain," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 138(3), pages 873-900, August.
    4. Imam, M. F. & Islam, Mohammad Amirul & Alam, M. A. & Hossain, M. Jamal. & Das, Sumonkanti, 2020. "Small Area Estimation Of Poverty In Rural Bangladesh," Bangladesh Journal of Agricultural Economics, Bangladesh Agricultural University, vol. 40(1&2), February.
    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. Stefano Marchetti & Maciej Beręsewicz & Nicola Salvati & Marcin Szymkowiak & Łukasz Wawrowski, 2018. "The use of a three‐level M‐quantile model to map poverty at local administrative unit 1 in Poland," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1077-1104, October.
    7. Angelo Moretti & Natalie Shlomo & Joseph W. Sakshaug, 2020. "Multivariate Small Area Estimation of Multidimensional Latent Economic Well‐being Indicators," International Statistical Review, International Statistical Institute, vol. 88(1), pages 1-28, April.
    8. Marchetti Stefano & Tzavidis Nikos, 2021. "Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas," Journal of Official Statistics, Sciendo, vol. 37(4), pages 955-979, December.
    9. 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.
    10. Isabel Molina & Paul Corral & Minh Nguyen, 2022. "Estimation of poverty and inequality in small areas: review and discussion," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1143-1166, December.
    11. Angelo Moretti & Natalie Shlomo & Joseph W. Sakshaug, 2021. "Small Area Estimation of Latent Economic Well-being," Sociological Methods & Research, , vol. 50(4), pages 1660-1693, November.
    12. Penelope Bilton & Geoff Jones & Siva Ganesh & Stephen Haslett, 2020. "Regression trees for poverty mapping," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(4), pages 426-443, December.
    13. Zhang, Xingmin & Zhang, Shuai, 2021. "Optimal time-varying tail risk network with a rolling window approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    14. 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.
    15. Francesco Schirripa Spagnolo & Antonella D’Agostino & Nicola Salvati, 2018. "Measuring differences in economic standard of living between immigrant communities in Italy," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1643-1667, July.

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