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


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


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

    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. Chris Elbers & Jean O. Lanjouw & Peter Lanjouw, 2003. "Micro--Level Estimation of Poverty and Inequality," Econometrica, Econometric Society, vol. 71(1), pages 355-364, January.
    3. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    4. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238.
    5. Ray Chambers & Nikos Tzavidis, 2006. "M-quantile models for small area estimation," Biometrika, Biometrika Trust, vol. 93(2), pages 255-268, June.
    6. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    7. Kokic, Philip, et al, 1997. "A Measure of Production Performance," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 445-451, October.
    8. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
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    1. repec:eee:csdana:v:115:y:2017:i:c:p:53-66 is not listed on IDEAS
    2. repec:spr:stmapp:v:26:y:2017:i:4:d:10.1007_s10260-017-0380-4 is not listed on IDEAS


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