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http://dx.doi.org/10.7465/jkdi.2014.25.4.941

Estimating small area proportions with kernel logistic regressions models  

Shim, Jooyong (Department of Data Science, Inje University)
Hwang, Changha (Department of Applied Statistics, Dankook University)
Publication Information
Journal of the Korean Data and Information Science Society / v.25, no.4, 2014 , pp. 941-949 More about this Journal
Abstract
Unit level logistic regression model with mixed effects has been used for estimating small area proportions, which treats the spatial effects as random effects and assumes linearity between the logistic link and the covariates. However, when the functional form of the relationship between the logistic link and the covariates is not linear, it may lead to biased estimators of the small area proportions. In this paper, we relax the linearity assumption and propose two types of kernel-based logistic regression models for estimating small area proportions. We also demonstrate the efficiency of our propose models using simulated data and real data.
Keywords
Logistic regression; mixed effect; proportion; small area estimation; spatial effect; support vector machine;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
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1 Cho, D. H., Shim, J. and Seok, K. H. (2010). Doubly penalized kernel method for heteroscedastic autoregressive data. Journal of the Korean Data & Information Science Society, 21, 155-162.   과학기술학회마을
2 Genton, M. G. (2001). Classes of kernels for machine learning: a statistics perspective. Journal of Machine Learning Research, 2, 299-312.
3 Hwang, C. and Shim, J. (2012). Smoothing Kaplan-Meier estimate using monotone suppot vector regression. Journal of the Korean Data & Information Science Society, 23, 1045-1054.   DOI   ScienceOn
4 Jiang, J. and Lahiri, P. (2006). Mixed model prediction and small area estimation. Test, 15, 1-96.   DOI
5 Kimeldorf, G. and Wahba, G. (1971). Some results on Tchebychean spline functions. Journal of Mathematical Analysis and Applications, 33, 82-95.   DOI
6 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.
7 Opsomer, J. D., Claeskens, G., Ranalli, M. G., Kauemann, G. and Breidt, F. J. (2008). Non-parametric small area estimation using penalized spline regression. Journal of the Royal Statistical Society B, 70, 265-286.   DOI   ScienceOn
8 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.   DOI   ScienceOn
9 Pfeffermann, D. (2013). New important developments in small area estimation. Statistical Science, 28, 40-68.   DOI
10 Rao, J. N. K. (2003). Small area estimation, Wiley, New York.
11 Shim, J. (2012). Kernel Poisson regression for mixed input variables. Journal of the Korean Data & Information Science Society, 23, 1231-1239.   과학기술학회마을   DOI   ScienceOn
12 Shim, J. and Hwang, C. (2012). M-quantile kernel regression for small area estimation. Journal of the Korean Data & Information Science Society, 23, 794-756.   과학기술학회마을   DOI   ScienceOn
13 Shim, J. and Hwang, C. (2013). Expected shortfall estimation using kernel machines. Journal of the Korean Data & Information Science Society, 24, 625-636.   과학기술학회마을   DOI   ScienceOn
14 Shim, J., Kim, Y. and Hwang, C. (2013). Generalized kernel estimating equation for panel estimation of small area unemployment rates. Journal of the Korean Data & Information Science Society, 24, 1199-1210.   과학기술학회마을   DOI   ScienceOn
15 Vapnik, V. N. (1995). The nature of statistical learning theory, Springer, New York.
16 Aradhye, H. and Dorai, C. (2002). New kernels for analyzing multimodal data in multimedia using kernel machines. Proceedings of the IEEE International Conference on Multimedia and Expo, 2, 37-40.