Non-parametric bootstrap mean squared error estimation for M-quantile estimators of small area averages, quantiles and poverty indicators
Non-parametric bootstrap mean squared error estimation for M-quantile estimators of small area averages, quantiles and poverty indicators
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.
chambers–dunstan estimator, income distribution, domain estimation, poverty mapping, resampling methods, robust estimation
2889-2902
Marchetti, Stefano
d47d90a9-90d3-40fa-b290-322caf8ee283
Tzavidis, Nikos
431ec55d-c147-466d-9c65-0f377b0c1f6a
Pratesi, Monica
d7fd7c86-3f2d-42ca-826c-c6d0f0a2a00a
October 2012
Marchetti, Stefano
d47d90a9-90d3-40fa-b290-322caf8ee283
Tzavidis, Nikos
431ec55d-c147-466d-9c65-0f377b0c1f6a
Pratesi, Monica
d7fd7c86-3f2d-42ca-826c-c6d0f0a2a00a
Marchetti, Stefano, Tzavidis, Nikos and Pratesi, Monica
(2012)
Non-parametric bootstrap mean squared error estimation for M-quantile estimators of small area averages, quantiles and poverty indicators.
[in special issue: Small Area Estimation]
Computational Statistics & Data Analysis, 56 (10), .
(doi:10.1016/j.csda.2012.01.023).
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.
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Submitted date: January 2012
e-pub ahead of print date: 9 February 2012
Published date: October 2012
Additional Information:
The 3rd Special Issue on Optimization Heuristics in Estimation and Modelling Problems
Keywords:
chambers–dunstan estimator, income distribution, domain estimation, poverty mapping, resampling methods, robust estimation
Identifiers
Local EPrints ID: 181971
URI: http://eprints.soton.ac.uk/id/eprint/181971
ISSN: 0167-9473
PURE UUID: bb28a855-8870-4212-9a4d-8669e6809952
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Date deposited: 27 Apr 2011 14:43
Last modified: 15 Mar 2024 03:11
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Author:
Stefano Marchetti
Author:
Monica Pratesi
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