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Robust varying coefficient model using L1 regularization
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 Title & Authors
Robust varying coefficient model using L1 regularization
Hwang, Changha; Bae, Jongsik; Shim, Jooyong;
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 Abstract
In this paper we propose a robust version of varying coefficient models, which is based on the regularized regression with L1 regularization. We use the iteratively reweighted least squares procedure to solve L1 regularized objective function of varying coefficient model in locally weighted regression form. It provides the efficient computation of coefficient function estimates and the variable selection for given value of smoothing variable. We present the generalized cross validation function and Akaike information type criterion for the model selection. Applications of the proposed model are illustrated through the artificial examples and the real example of predicting the effect of the input variables and the smoothing variable on the output.
 Keywords
Akaike`s information criterion;generalized cross validation function;iteratively reweighted least squares procedure;L1-regularization;locally weighted regression;smoothing variable;variable selection;varying coefficient model;
 Language
English
 Cited by
 References
1.
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transaction on Automatic Control, 19, 716-723. crossref(new window)

2.
Cho, D. H., Shim, J. and Seok, K. (2010). Doubly regularized kernel method for heteroscedastic autoregressive data. Journal of the Korean Data & Information Science Society, 21, 155-162.

3.
Cleveland, W. S. and Devlin, S. J. (1988). Locally-weighted regression: An approach to regression analysis by local fitting. Journal of the American Statistical Associationl, 83, 596-610. crossref(new window)

4.
Fan, J. and I. Gijbels (1996). Local polynomial modelling and its applications, Chapman & Hall, Boca Raton.

5.
Fan, J. and Zhang, W. (2008). Statistical methods with varying coefficient models. Statistics and its Inter-face, 1, 179-195. crossref(new window)

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. crossref(new window)

8.
Hu, S. and Rao, J. S. (2010). Sparse penalization with censoring constraints for estimating high dimensional AFT models with applications to microarray data analysis, Technical Report 07 of Division of Biostatistics, Case Western Reserve University, Ohio.

9.
Huang, J., Ma, S. and Xie, H. (2005). Regularized estimation in the accelerated failure time model with high dimensional covariates, Technical Report No. 349, Department of Statistics and Actuarial Science, The University of Iowa, Iowa.

10.
Hwang, C., Kim, M. and Shim, J. (2011). Variable selection in L1 penalized censored Regression. Journal of the Korean Data & Information Science Society, 22, 951-959.

11.
Krishnapuram, B., Carlin, L., Figueiredo, M. A. T. and Hartermink, A. J. (2005). Sparse multinomial logistic regression: Fast algorithms and generalization bounds. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 957-968. crossref(new window)

12.
Park, B. U., Mammen, E., Lee, Y. K. and Lee, E. R. (2015). Varying coefficient regression models: A review and new developments. International Statistical Review, 83, 36-64. crossref(new window)

13.
Sauerbrei, W. and Schumacher, M. (1992). A bootstrap resampling procedure for model building: Application to the Cox regression model. Statistical Medicine, 11, 2093-2099. crossref(new window)

14.
Shim, J. and Hwang, C. (2015). Varying coefficient modeling via least squares support vector regression. Neurocomputing, 161, 254-259. crossref(new window)

15.
Shim, J., Kim, M. and Seok, K. (2015). SVQR with asymmetric quadratic function. Journal of the Korean Data & Information Science Society, 26, 1537-1545. crossref(new window)

16.
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society B, 58, 267-288.

17.
Wang, H. and Xia, Y. (2009). Shrinkage Estimation of the varying coefficient model. Journal of the American Statistical Association, 104, 747-757. crossref(new window)

18.
Williams, P. M. (1995). Bayesian regularization and pruning using a Laplace prior. Neural Computation, 7, 117-143. crossref(new window)

19.
Wooldridge, J. M. (2012).Introductory econometrics: A modern approach, South-Western Cengage Learning, Mason.

20.
Wu, C., Shi, X., Cui, Y. and Ma, S. (2015). A penalized robust semiparametric approach for gene-environment interactions. Statistics in Medicine, doi:10.1002/sim.6609. crossref(new window)