Comparative Performance of Spatial Robust Small Area Estimation Methods: A Simulation Study
Abstract
Estimating parameters for small areas often faces limitations due to insufficient sample sizes, resulting in low-precision estimates. The Small Area Estimation (SAE) approach is used to address this problem by utilizing auxiliary variables to improve estimation efficiency. This study evaluates four SAE methods, namely EBLUP, REBLUP, SEBLUP, and SREBLUP, through a simulation study based on a nested error model across 18 scenarios that combine two area sizes (16 and 64 areas), levels of outlier contamination in the error component, and degrees of spatial correlation in the area-level random effects. Each scenario is replicated 50 times. Model performance is evaluated using Relative Bias (RB) and Relative Root Mean Square Error (RRMSE). The results show that non-robust methods are sensitive to outliers, whereas robust methods produce more stable estimates. The SREBLUP method demonstrates the best performance under low to moderate spatial correlation. In addition, an ANOVA test is conducted to identify factors that significantly affect the response.
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C. Baldermann, N. Salvati, and T. Schmid, “Robust small area estimation under spatial non-stationarity,” International Statistical Review, vol. 86, no. 1, pp. 136–159, Apr. 2018, doi: 10.1111/insr.12245.
S. K. ’Sinha and J. N. K. ’Rao, “Robust small area estimation,” Can J Statistics, vol. 37, pp. 381–399, 2009.
J. N. K. Rao and I. Molina, “Small area estimation”. Hoboken, NJ: Wiley.
A. Petrucci, M. Pratesi, and N. Salvati, “Geographic information in small area estimation: small area models and spatially correlated random area effects,” 2005.
N. A. C. Cressie, “Statistics for spatial data”. New York: Wiley, 1993.
J. N. K. Rao, “Small Area Estimation,” New York: Wiley , 2003. doi: DOI:10.1002/0471722189.
N. Salvati, “Small Area Estimation by Spatial Mo dels: the Spatial Empirical Best Linear Unbiased Prediction (Spatial EBLUP).” 2004. Working Paper, University of Pisa.
N. Wichitaksorn, S. T. B. Choy, and R. Gerlach, “A generalized class of skew distributions and associated robust quantile regression models,” Canadian Journal of Statistics, p. n/a-n/a, Sep. 2014, doi: 10.1002/cjs.
T. Schmid, N. Tzavidis, R. Münnich, and R. Chambers, “Outlier robust small-area estimation under spatial correlation,” Scandinavian Journal of Statistics, vol. 43, no. 3, pp. 806–826, 2016, doi: 10.1111/sjos.12205.
T. Schmid and R. T. Münnich, “Spatial robust small area estimation,” Statistical Papers, vol. 55, no. 3, pp. 653–670, 2014, doi: 10.1007/s00362-013-0517-y.
G. Fauziah, A. Kurnia, and A. Djuraidah, “The empirical best linear unbiased prediction and the emperical best predictor unit-level approaches in estimating per capita expenditure at the subdistrict level,” Scientific Journal of Informatics, vol. 12, no. 2, pp. 283–294, Jun. 2025, doi: 10.15294/sji.v12i2.25037.
N. H. Pusponegoro and R. N. Rachmawati, “Spatial empirical best linear unbiased prediction in small area estimation of poverty,” in Procedia Computer Science, Elsevier B.V., 2018, pp. 712–718. doi: 10.1016/j.procs.2018.08.214.
N. Rakhsyanda, K. Sadik, and I. Indahwati, “Simulation study of robust geographically weighted empirical best linear unbiased predictor on small area estimation,” Indonesian Journal of Statistics and Its Applications, vol. 5, no. 1, pp. 50–60, Mar. 2021, doi: 10.29244/ijsa.v5i1p50-60.
A. Apriliansyah and I. Y. Wulansari, “Application of Spatial Empirical Best Linear Unbiased Prediction (SEBLUP) of Open Unemployment Rate on Sub-District Level Estimation in Banten Province”, icdsos, vol. 2021, no. 1, pp. 905–913, Jan. 2022.
A. Salma, K. Sadik, and K. A. Notodiputro, “Small area estimation of per capita expenditures using robust empirical best linear unbiased prediction (REBLUP),” in AIP Conference Proceedings, American Institute of Physics Inc., Mar. 2017. doi: 10.1063/1.4979443.
R. E. Fay, R. A. Herriot, and R. E. F. Iii, “Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data,” 1979.
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 Am Stat Assoc, vol. 83, no. 401, p. 28, Mar. 1988, doi: 10.2307/2288915.
C. R. ’Henderson, “Best linear unbiased estimation and prediction under a selection model,” Biometrics, vol. 31, no. 2, pp. 423–47, 1975.
D. A. ’Harville, “Maximum likelihood approaches to variance component estimation and to related problems,” J Am Stat Assoc, vol. 72, no. 358, pp. 320–338, 1977.
W. H. Fellner, “Robust estimation of variance components,” Technometrics, 28, 51-60. https://doi.org/10.1080/00401706.1986.104880971986.
H. Li, Y. Liu, and R. Zhang, “Small area estimation under transformed nested-error regression models,” Statistical Papers, vol. 60, no. 4, pp. 1397–1418, Aug. 2019, doi: 10.1007/s00362-017-0879-7.
P. A. Parker, R. Janicki, and S. H. Holan, “A comprehensive overview of unit-level modeling of survey data for small area estimation under informative sampling,” J Surv Stat Methodol, vol. 11, no. 4, pp. 829–857, Sep. 2023, doi: 10.1093/jssam/smad020.
L. ’Mori and M. R. ’Ferrante, “Small area estimation of household economic indicators under unit-level generalized additive models for location, scale and shape,” J Surv Stat Methodol, vol. 13, no. 1, pp. 160–196, 2025.
DOI: http://dx.doi.org/10.30829/zero.v9i3.26477
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