Simulation Study of Robust Geographically Weighted Empirical Best Linear Unbiased Predictor on Small Area Estimation

Simulasi Metode Prediksi Tak Bias Linier Terbaik Empiris Terboboti Geografis Kekar pada Pendugaan Area Kecil

Authors

  • Naima Rakhsyanda Department of Statistics, IPB University, Indonesia
  • Kusman Sadik Department of Statistics, IPB University, Indonesia
  • Indahwati Department of Statistics, IPB University, Indonesia

DOI:

https://doi.org/10.29244/ijsa.v5i1p50-60

Abstract

Small area estimation can be used to predict the population parameter with small sample sizes. For some cases, the population units that are close spatially may be more related than units that are further apart. The use of spatial information like geographic coordinates are studied in this research. Outlier contaminations can affect small area estimations. This study was conducted using simulation methods on generated data with six scenarios. The scenarios are the combination of spatial effects (spatial stationary and spatial non-stationary) with outlier contamination (no outlier, symmetric outliers, and non-symmetric outliers). The purpose of this study was to compare the geographically weighted empirical best linear unbiased predictor (GWEBLUP) and robust GWEBLUP (RGWEBLUP) with direct estimator, EBLUP, and REBLUP using simulation data. The performance of the predictors is evaluated using relative root mean squared error (RRMSE). The simulation results showed that geographically weighted predictors have the smallest RRMSE values for scenarios with spatial non-stationary, therefore offer a better prediction. For scenarios with outliers, robust predictors with smaller RRMSE values offer more efficiency than non-robust predictors.

Downloads

Download data is not yet available.

References

Baldermann, C., Salvati, N., & Schmid, T. (2018). Robust Small Area Estimation under Spatial Non-stationarity: Robust SAE under Spatial Non-Stationarity. International Statistical Review, 86(1), 136–159.

Brunsdon, C., Fotheringham, A. S., & Charlton, M. E. (1996). Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity. Geographical Analysis, 28(4), 281–298.

Chambers, R., Chandra, H., Salvati, N., & Tzavidis, N. (2014). Outlier robust small area estimation. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(1), 47–69.

Chambers, R. L. (1986). Outlier Robust Finite Population Estimation. Journal of the American Statistical Association, 81(396), 1063–1069.

Chandra, H., Salvati, N., Chambers, R., & Tzavidis, N. (2012). Small area estimation under spatial nonstationarity. Computational Statistics & Data Analysis, 56(10), 2875–2888.

Draper, N. R., & Smith, H. (1998). Applied Regression Analysis. New York (US): John Wiley & Sons.

Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Chichester (UK): John Wiley & Sons.

Liu, Y., & Zumbo, B. D. (2007). The Impact of Outliers on Cronbach’s Coefficient Alpha Estimate of Reliability: Visual Analogue Scales. Educational and Psychological Measurement, 67(4), 620–634.

Pratesi, M., & Salvati, N. (2008). Small area estimation: The EBLUP estimator based on spatially correlated random area effects. Statistical Methods and Applications, 17(1), 113–141.

Rao, J. N. K. (2003). Small area estimation. New York (US): John Wiley & Sons.

Sadik, K. (2009). Metode Prediksi Tak-bias Linear Terbaik dan Bayes Berhirarki untuk Pendugaan Area Kecil Berdasarkan Model State Space [disertasi]. Bogor (ID): Institut Pertanian Bogor.

Schmid, T., & Münnich, R. T. (2014). Spatial robust small area estimation. Statistical Papers, 55(3), 653–670.

Schmid, T., Tzavidis, N., Münnich, R., & Chambers, R. (2016). Outlier Robust Small-Area Estimation Under Spatial Correlation: Spatial robust small-area estimation. Scandinavian Journal of Statistics, 43(3), 806–826.

Sinha, S. K., & Rao, J. N. K. (2009). Robust small area estimation. Canadian Journal of Statistics, 37(3), 381–399.

Downloads

Published

2021-03-31

How to Cite

Rakhsyanda, N., Sadik, K., & Indahwati, I. (2021). Simulation Study of Robust Geographically Weighted Empirical Best Linear Unbiased Predictor on Small Area Estimation: Simulasi Metode Prediksi Tak Bias Linier Terbaik Empiris Terboboti Geografis Kekar pada Pendugaan Area Kecil. Indonesian Journal of Statistics and Its Applications, 5(1), 50–60. https://doi.org/10.29244/ijsa.v5i1p50-60

Issue

Section

Articles