Journal of the Korean Data and Information Science Society

한국데이터정보과학회 (The Korean Data and Information Science Society)
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Geographically weighted kernel logistic regression for small area proportion estimation

  • 투고 : 2016.01.15
  • 심사 : 2016.03.22
  • 발행 : 2016.03.31
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초록

In this paper we deal with the small area estimation for the case that the response variables take binary values. The mixed effects models have been extensively studied for the small area estimation, which treats the spatial effects as random effects. However, when the spatial information of each area is given specifically as coordinates it is popular to use the geographically weighted logistic regression to incorporate the spatial information by assuming that the regression parameters vary spatially across areas. In this paper, relaxing the linearity assumption and propose a geographically weighted kernel logistic regression for estimating small area proportions by using basic principle of kernel machine. Numerical studies have been carried out to compare the performance of proposed method with other methods in estimating small area proportion.

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참고문헌

  1. Anselin, L. (1992). Spatial econometrics: Method and models, Kluwer Academic Publishers, Boston.
  2. Brunsdon, C., Fotheringham, A. S. and Charlton, M. (1996). Geographically weighted regression: A method for exploring spatial nonstationarity. Geographical Analysis, 28, 281-298.
  3. Harville, D. A. (1976). Extension of Gauss-Markov theorem to include the estimation of random effects. Annals of Statistics, 4, 384-395. https://doi.org/10.1214/aos/1176343414
  4. Hwang, H. (2014). Support vector quantile regression for autoregressive data. Journal of the Korean Data & Information Science Society,25, 1539-1547. https://doi.org/10.7465/jkdi.2014.25.6.1539
  5. Hwang, H. (2015). Partially linear support vector orthogonal quantile regression with measurement errors. Journal of the Korean Data & Information Science Society, 26, 209-216. https://doi.org/10.7465/jkdi.2015.26.1.209
  6. Jiang, J. and Lahiri, P. (2006). Mixed model prediction and small area estimation. Test, 15, 1-96. https://doi.org/10.1007/BF02595419
  7. Kimeldorf, G. and Wahba, G. (1971). Some results on Tchebychean spline functions. Journal of Mathematical Analysis and Applications, 33, 82-95. https://doi.org/10.1016/0022-247X(71)90184-3
  8. Mercer, J. (1909). Functions of positive and negative type and their connection with theory of integral equations. Philosophical Transactions of Royal Society A, 415-446.
  9. Perez-Cruz, F., Bousono-Calzon, C. and Artes-Rodriguez, A. (2005). Convergence of the IRWLS procedures to SVM solution. Neural Computation, 17, 7-18. https://doi.org/10.1162/0899766052530875
  10. Pfeffermann, D, (2013). New important developments in small area estimation. Statistical Science, 28, 40-68. https://doi.org/10.1214/12-STS395
  11. Rao, J. N. K. (2003). Small area estimation, Wiley, New York.
  12. Rifkin, R. and Klautau, A. (2004). In defense of one-vs-all classification. Journal of Machine Learning Research, 5, 101-141.
  13. Salvati, N., Ranalli, M. G. and Pratesi, M. (2011). Small area estimation of the mean using non-parametric M-quantile regression: A comparison when a linear mixed model does not hold. Journal of Statistical Computation and Simulation, 81, 945- 964. https://doi.org/10.1080/00949650903575237
  14. Seok, K. (2015). Semisupervised support vector quantile regression. Journal of the Korean Data & Information Science Society, 26, 517-524. https://doi.org/10.7465/jkdi.2015.26.2.517
  15. Shim, J. and Hwang, C. (2014). Estimating small area proportions with kernel logistic regressions models. Journal of the Korean Data & Information Science Society, 25, 941-949. https://doi.org/10.7465/jkdi.2014.25.4.941
  16. Shim, J. and Seok, K. H. (2014). A transductive least squares support vector machine with the difference convex algorithm. Journal of the Korean Data & Information Science Society, 25, 455-464. https://doi.org/10.7465/jkdi.2014.25.2.455
  17. Suykens, J. A. K. and Vandewalle, J. (1999). Least squares support vector machine classiers. Neural Processing Letters, 9, 293-300. https://doi.org/10.1023/A:1018628609742
  18. Vapnik, V. N. (1995). The nature of statistical learning theory, Springer, New York.
  19. Vapnik, V. N. (1998). Statistical learning theory, Springer, New York.
  20. Yu, D. L. and Wu, C. (2004) Understanding population segregation from Landsat ETM+imagery: A geographically weighted regression approach. GISience and Remote Sensing, 41, 145-164.