Comparison of mean squared error estimators under the Fay-Herriot model: application to poverty and percentage of food expenditure data

Year 2020, Volume: 49 Issue: 1, 439 - 457, 06.02.2020

Yegnanew A Shiferaw , Jacqueline Galpin

https://doi.org/10.15672/hujms.516601

Cited By: 1

Abstract

Small area estimates have received much attention from both private and public sectors due to the growing demand for effective planning of health services, apportioning of government funds and policy and decision making. The uncertainty of empirical best linear unbiased predictor (EBLUP) estimates is widely assessed by mean squared error (MSE). MSEs are criticized as they are not area specific since they do not depend on the direct estimators from the survey. In this paper, we compare the performances of different MSE estimators with respect to the relative bias and relative risk using a Monte Carlo simulation study.  Simulation results suggest the superiority of the proposed MSEs over the existing methods in some situations. As a case study, the 2010/11 household consumption expenditure survey (HCES) and the 2007 housing and population census of Ethiopia have been used to study the performances of the MSE estimators.

Keywords

Area-specific, EBLUP estimator, Fay-Herriot model, MSE estimator

References

• [1] R. Ananya, Empirical and Hierarchical Bayesian Methods with Applications to Small Area Estimation, PhD Dissertation, University of Florida, 2007.
• [2] G.E. Battese, R.M. Harter and W.A. Fuller, An error components model for prediction of county crop areas using survey and satellite data, J. Amer. Statist. Assoc. 83, 28-36, 1988.
• [3] A. Bianchi, E. Fabrizi, N. Salvati and N. Tzavidis, Estimation and testing in Mquantile regression with applications to small area estimation, Int. Stat. Rev. 86, 541-570, 2018.
• [4] D. R. Cox, A Prediction intervals and empirical Bayes confidence intervals. In Perspectives in probability and statistics, Papers in honor of M.S. Bartlett (ed. J. Gani), 47-55, Academic Press, London, 1975.
• [5] G.S. Datta and P. Lahiri, A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems, Statist. Sinica 10, 613-627, 2000.
• [6] G.S. Datta, J.N.K. Rao, and D.D. Smith, On measuring the variability of small area estimators under a basic area level model, Biometrika 92, 183-196, 2005.
• [7] G.S. Datta, T. Kubokawa, I. Molina, and J.N.K. Rao, Estimation of mean squared error of model-based small area estimators, Test 20, 367-388, 2011.
• [8] M.D. Esteban, D. Morales, A. Perez and L. Santamaria, Small area estimation of poverty proportions under area-level time models, Comput. Statist. Data Anal. 56, 2840-2855, 2012.
• [9] R. E. Fay and R.A. Herriot, Estimates of income for small places: An application of James-Stein procedure to census data, J. Amer. Statist. Assoc. 74, 269-277, 1979.
• [10] J. Foster, J. Greer, and E. Thorbecke, A class of decomposable poverty measures, Econometrica 52, 761-766, 1984.
• [11] J. Jiang and P. Lahiri, Mixed model prediction and small area estimation, Test 15, 1-96, 2006.
• [12] T. Kubokawa and B. Nagashima, Parametric bootstrap methods for bias correction in linear mixed models, J. Multivariate Anal. 106, 1-16, 2012.
• [13] H. Li, Small area estimation: An empirical best linear unbiased predictor approach. PhD dissertation, University of Maryland, United States, 2007.
• [14] H. Li and P. Lahiri, An adjusted maximum likelihood method for solving small area estimation problems, J. Multivariate Anal. 101, 882 - 892, 2010.
• [15] MoFED, Ethiopia’s progress towards eradicating poverty: an interim report on poverty analysis study, Development Planning and Research Directorate, Addis Ababa, Ethiopia, 2012.
• [16] I. Molina, J.N.K. Rao and G.S. Data, Small area estimation under a Fay-Herriot model with preliminary testing for the presence of random effects, Survey Methodology 41, 1-19, 2015.
• [17] N.G.N. Prasad and J. N. K. Rao, The estimation of the mean squared error of small area estimators, J. Amer. Statist. Assoc. 85, 163-171, 1990.
• [18] M. Pratesi, Analysis of poverty data by small area estimation, John Wiley and Sons, 2015.
• [19] J.N.K. Rao, EB and EBLUP in small area estimation in S. E. Ahmed and N. Reid (Eds.); Empirical Bayes and Likelihood Inference, Lecture Notes in Statistics 148, New York: Springer, 33-43, 2001.
• [20] J.N.K Rao and I. Molina, Small Area Estimation. John Wiley and Sons, Inc., New York, 2015.
• [21] L.P. Rivest and E. Belmonte, A Conditional Mean Squared Error of Small Area Estimators, Survey Methodology 26, 79-90, 2000.
• [22] Y.A. Shiferaw and J.S. Galpin, Area specific confidence intervals for a small area mean under the Fay-Herriot model, J. Iran. Stat. Soc. 15, 1-44, 2016.
• [23] Y. Shiferaw and J. Galpin, A corrected confidence interval for a small area parameter through the weighted estimator under the basic area level model, J. Iran. Stat. Soc. 18, 17-51, 2019.
• [24] Y.A. Shiferaw and J.S. Galpin, Improved confidence intervals for a small area mean under the Fay-Herriot model, Accessed from wiredspace.wits.ac.za.
• [25] Q. Yanping, G.D. Meeden and B. Zhang, An objective stepwise Bayes approach to small area estimation, J. Stat. Comput. Simul. 85, 1474-1494, 2015.
• [26] M. Yoshimori and P. Lahiri, A second-order efficient empirical Bayes confidence interval, Ann. Statist. 42, 1233-1261, 2014.