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

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), 2889-2902. (doi:10.1016/j.csda.2012.01.023).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/j.csda.2012.01.023
Additional Information: The 3rd Special Issue on Optimization Heuristics in Estimation and Modelling Problems
ISSNs: 0167-9473 (print)
Keywords: chambers–dunstan estimator, income distribution, domain estimation, poverty mapping, resampling methods, robust estimation
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HN Social history and conditions. Social problems. Social reform
Divisions : University Structure - Pre August 2011 > School of Social Sciences > Social Statistics
ePrint ID: 181971
Accepted Date and Publication Date:
October 2012Published
9 February 2012Made publicly available
2012In press
January 2012Submitted
Date Deposited: 27 Apr 2011 14:43
Last Modified: 31 Mar 2016 13:36

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