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

2012 ◽  
Vol 56 (10) ◽  
pp. 2889-2902 ◽  
Author(s):  
Stefano Marchetti ◽  
Nikos Tzavidis ◽  
Monica Pratesi
Keyword(s):  
Error Estimation ◽  
Small Area ◽  
Mean Squared Error ◽  
Parametric Bootstrap ◽  
Squared Error ◽  
Quantile Estimators ◽  
Poverty Indicators ◽  
Non Parametric

scholarly journals Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas

2021 ◽  
Vol 37 (4) ◽  
pp. 955-979
Author(s):  
Stefano Marchetti ◽  
Nikos Tzavidis
Keyword(s):  
Gini Coefficient ◽  
Small Area ◽  
Mean Squared Error ◽  
Small Area Estimation ◽  
Parametric Bootstrap ◽  
Theil Index ◽  
Error Estimator ◽  
Area Estimation ◽  
Squared Error ◽  
The Gini Coefficient

Abstract Small area estimation is receiving considerable attention due to the high demand for small area statistics. Small area estimators of means and totals have been widely studied in the literature. Moreover, in the last years also small area estimators of quantiles and poverty indicators have been studied. In contrast, small area estimators of inequality indicators, which are often used in socio-economic studies, have received less attention. In this article, we propose a robust method based on the M-quantile regression model for small area estimation of the Theil index and the Gini coefficient, two popular inequality measures. To estimate the mean squared error a non-parametric bootstrap is adopted. A robust approach is used because often inequality is measured using income or consumption data, which are often non-normal and affected by outliers. The proposed methodology is applied to income data to estimate the Theil index and the Gini coefficient for small domains in Tuscany (provinces by age groups), using survey and Census micro-data as auxiliary variables. In addition, a design-based simulation is carried out to study the behaviour of the proposed robust estimators. The performance of the bootstrap mean squared error estimator is also investigated in the simulation study.

scholarly journals Parametric bootstrap mean squared error of a small area multivariate EBLUP

2018 ◽  
Vol 49 (6) ◽  
pp. 1474-1486 ◽  
Author(s):  
Angelo Moretti ◽  
Natalie Shlomo ◽  
Joseph W. Sakshaug
Keyword(s):  
Small Area ◽  
Mean Squared Error ◽  
Parametric Bootstrap ◽  
Squared Error

Optimal choice between parametric and non-parametric bootstrap estimates

1994 ◽  
Vol 115 (2) ◽  
pp. 335-363 ◽  
Author(s):  
Stephen Man Sing Lee
Keyword(s):  
Mean Squared Error ◽  
Parametric Bootstrap ◽  
Tuning Parameter ◽  
Squared Error ◽  
Optimal Estimator ◽  
Bootstrap Estimate ◽  
The Mean ◽  
Bootstrap Estimates ◽  
Hybrid Estimator ◽  
Non Parametric

AbstractA parametric bootstrap estimate (PB) may be more accurate than its non-parametric version (NB) if the parametric model upon which it is based is, at least approximately, correct. Construction of an optimal estimator based on both PB and NB is pursued with the aim of minimizing the mean squared error. Our approach is to pick an empirical estimate of the optimal tuning parameter ε∈[0, 1] which minimizes the mean square error of εNB+(1−ε) PB. The resulting hybrid estimator is shown to be more reliable than either PB or NB uniformly over a rich class of distributions. Theoretical asymptotic results show that the asymptotic error of this hybrid estimator is quite close in distribution to the smaller of the errors of PB and NB. All these errors typically have the same convergence rate of order . A particular example is also presented to illustrate the fact that this hybrid estimate can indeed be strictly better than either of the pure bootstrap estimates in terms of minimizing mean squared error. Two simulation studies were conducted to verify the theoretical results and demonstrate the good practical performance of the hybrid method.

scholarly journals Attack-resilient minimum mean-squared error estimation

2014 ◽  
Author(s):  
James Weimer ◽  
Nicola Bezzo ◽  
Miroslav Pajic ◽  
Oleg Sokolsky ◽  
Insup Lee
Keyword(s):  
Error Estimation ◽  
Mean Squared Error ◽  
Minimum Mean Squared Error ◽  
Squared Error

Bootstrap mean squared error of a small-area EBLUP

2008 ◽  
Vol 78 (5) ◽  
pp. 443-462 ◽  
Author(s):  
W. González-Manteiga ◽  
M. J. Lombardía ◽  
I. Molina ◽  
D. Morales ◽  
L. Santamaría
Keyword(s):  
Small Area ◽  
Mean Squared Error ◽  
Squared Error
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