SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 1

Comparison of mean squared error estimatorsunder the Fay-Herriot model: application topoverty and percentage of food expenditure data

Yegnanew A. SHİFERAW
Jacqueline S. GALPİN
Pages
439–457
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this paper, we compare the performances of different MSE estimatorswith 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 methodsin some situations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Small area estimates have received much attention from both private and public sectors dueto the growing demand for effective planning of health services, apportioning of governmentfunds and policy and decision making.
📊
Key Findings & Data:In this paper, we compare the performances of different MSE estimatorswith 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 methodsin some situations.
💡
Conclusion & Impact:As a case study, the 2010/11 household consumption expendituresurvey (HCES) and the 2007 housing and population census of Ethiopia have been usedto study the performances of the MSE estimators.
🔬Design:Survey & Empirical Study
📍Scope:2010 Verileri
⚙️Variables:Domain Parameters

Abstract

Small area estimates have received much attention from both private and public sectors dueto the growing demand for effective planning of health services, apportioning of governmentfunds and policy and decision making. The uncertainty of empirical best linear unbiasedpredictor (EBLUP) estimates is widely assessed by mean squared error (MSE). MSEs arecriticized as they are not area specific since they do not depend on the direct estimatorsfrom the survey. In this paper, we compare the performances of different MSE estimatorswith 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 methodsin some situations. As a case study, the 2010/11 household consumption expendituresurvey (HCES) and the 2007 housing and population census of Ethiopia have been usedto study the performances of the MSE estimators.

🔖

Cite This Article

SHİFERAW, Y. A., GALPİN, J. S. (2022). Comparison of mean squared error estimatorsunder the Fay-Herriot model: application topoverty and percentage of food expenditure data. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 439–457. https://ajindex.com/articles/529612

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (2)

  1. R. Ananya,Empirical and Hierarchical Bayesian Methods with Applications to SmallArea Estimation, PhD Dissertation, University of Florida, 2007. [2]G.E. Battese, R.M. Harter and W.A. Fuller,An error components model for predictionof 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 M-quantile 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. InPer-spectives in probability and statistics, Papers in honor of M.S. Bartlett (ed. J. Gani),47-55,
  2. Academic Press, London, 1975. [5]G.S. Datta and P. Lahiri,A unified measure of uncertainty of estimated best linearunbiased predictors in small area estimation problems, Statist. Sinica10, 613-627,2000. [6]G.S. Datta, J.N.K. Rao, and D.D. Smith,On measuring the variability of small areaestimators under a basic area level model, Biometrika92, 183-196, 2005. [7]G.S. Datta, T. Kubokawa, I. Molina, and J.N.K. Rao,Estimation of mean squarederror of model-based small area estimators, Test20, 367-388, 2011. [8]M.D. Esteban, D. Morales, A. Perez and L. Santamaria,Small area estimation ofpoverty 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 ofJames-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,Econometrica52, 761-766, 1984. [11]J. Jiang and P. Lahiri,Mixed model prediction and small area estimation, Test15,1-96, 2006. [12]T. Kubokawa and B. Nagashima,Parametric bootstrap methods for bias correction inlinear 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 areaestimation problems, J. Multivariate Anal.101, 882 - 892, 2010. [15]MoFED,Ethiopia’s progress towards eradicating poverty: an interim report on povertyanalysis 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-Herriotmodel with preliminary testing for the presence of random