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http://dx.doi.org/10.7465/jkdi.2017.28.5.971

Varying coefficient model with errors in variables  

Sohn, Insuk (Statistics and Data Center, Samsung Medical Center)
Shim, Jooyong (Department of Statistics, Inje University)
Publication Information
Journal of the Korean Data and Information Science Society / v.28, no.5, 2017 , pp. 971-980 More about this Journal
Abstract
The varying coefficient regression model has gained lots of attention since it is capable to model dynamic changes of regression coefficients in many regression problems of science. In this paper we propose a varying coefficient regression model that effectively considers the errors on both input and response variables, which utilizes the kernel method in estimating the varying coefficient which is the unknown nonlinear function of smoothing variables. We provide a generalized cross validation method for choosing the hyper-parameters which affect the performance of the proposed model. The proposed method is evaluated through numerical studies.
Keywords
Generalized cross validation function; kernel method; measurement error model; smoothing variable; varying coefficient regression model;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Boggs, P. T. and Rogers, J. E. (1990). Orthogonal distance regression. Contemporary Mathematics, 112, 183-194.
2 Carroll, R. J., Ruppert, D. and Stefanski, L. A. (1997). Measurement error in nonlinear models, Monographs on Statistics and Applied Probability, Chapman & Hall, New York.
3 Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross validation. Numerical Mathematics, 31, 377-403.
4 Fan, J. and Zhang, W. (2008). Statistical methods with varying coefficient models. Statistics and Its Interface, 1, 179-195.   DOI
5 Fuller, W. A. (1987). Measurement error models, Wiley, New York.
6 Hastie, T. and Tibshirani, R. (1993). Varying-coefficient models. Journal of the Royal Statistical Society: B, 55, 757-796.
7 Hoover, D. R., Rice, J. A., Wu, C. O. and Yang, L. P. (1998). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika, 85, 809-822.   DOI
8 Lee, Y. K., Mammen, E. and Park, B. U. (2012). Projection-type estimation for varying coefficient regression models. Bernoulli, 18, 177-205.   DOI
9 Li, Q. and Racine, J. S. (2010). Smooth varying-coefficient estimation and inference for qualitative and quantitative data. Econometric Theory, 26, 1607-1637.   DOI
10 Madansky, A. (1959). The fitting of straight lines when both variables are subject to error. Journal of the American Statistical Association, 54, 173-205.   DOI
11 Mercer, J. (1909). Function of positive and negative type and their connection with theory of integral equations. Philosophical Transactions of Royal Society A, 415-416.
12 Shim, J. (2014). Quantile regression with errors in variables. Journal of the Korean Data & Information Science Society, 25, 439-446.   DOI
13 Shim, J and Hwang, C. (2015). Varying coefficient modeling via least squares support vector regression. Neurocomputing, 161, 254-259.   DOI
14 Van Gorp, J., Schoukens, J. and Pintelon, R. (2000). Learning neural networks with noisy inputs using the errors-in-variables approach. IEEE Transactions on Neural Networks, 11, 402-414.   DOI
15 Wooldridge, J. M. (2003). Introductory econometrics: A modern approach, South-Western Cengage Learning, Mason.
16 Zhang, W., Lee, S. Y. and Song, X. (2002). Local polynomial fitting in semivarying coefficient models. Journal of Multivariate Analysis, 82, 166-188.   DOI
17 Xue, L. and Qu, A. (2012). Variable selection in high-dimensional varying-coefficient models with global optimality. Journal of Machine Learning Research, 13, 1973-1998.
18 Hu, Y. and Schennach, S. M. (2008). Identification and estimation of nonclassical nonlinear errors-invariables models with continuous distributions using instruments. Econometrica, 76, 195-216.   DOI