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http://dx.doi.org/10.7465/jkdi.2016.27.6.1653

Estimation and variable selection in censored regression model with smoothly clipped absolute deviation penalty  

Shim, Jooyong (Department of Statistics, Institute of Statistical Information, Inje University)
Bae, Jongsig (Department of Mathematics, Sungkyunkwan University)
Seok, Kyungha (Department of Statistics, Institute of Statistical Information, Inje University)
Publication Information
Journal of the Korean Data and Information Science Society / v.27, no.6, 2016 , pp. 1653-1660 More about this Journal
Abstract
Smoothly clipped absolute deviation (SCAD) penalty is known to satisfy the desirable properties for penalty functions like as unbiasedness, sparsity and continuity. In this paper, we deal with the regression function estimation and variable selection based on SCAD penalized censored regression model. We use the local linear approximation and the iteratively reweighted least squares algorithm to solve SCAD penalized log likelihood function. The proposed method provides an efficient method for variable selection and regression function estimation. The generalized cross validation function is presented for the model selection. Applications of the proposed method are illustrated through the simulated and a real example.
Keywords
Censored regression model; generalized cross validation function; iteratively reweighted least squares procedure; smoothly clipped absolute deviation penalty; variable selection;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Kim, J., Sohn, I., Kim, D. H., Son, D. S., Ahn, H. and Jung, S. H. (2013). Prediction of a time-to-event trait using genome wide SNP data. BMC Bioinformatics, 14, 58.   DOI
2 Koul, H., Susarla, V. and Van Ryzin, J. (1981). Regression analysis with randomly right censored data. The Annal of Statistics, 9, 1276-1288.   DOI
3 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.   DOI
4 Li, H. (2006). Censored data regression in high-dimension and low-sample size settings for genomic applications, UPenn Biostatistics Working Paper 9, University of Pennsylvania, PA, USA.
5 Orbe, J., Ferreira, E. and Nunez-Anton, V. (2003). Censored partial regression. Biostatistics, 4, 109-121.   DOI
6 Rosenwald, A., Wright, G., Chan, W. C., Connors, J. M., Campo, E., Fisher, R. I., Gascoyne, R. D., Muller-Hermelink, H. K., Smeland, E. B., Giltnane J. M. and et al. (2002). The use of molecular profiling to predict survival after chemotherapy for diffuse large-B-cell lymphoma. New England Journal of Medicine, 346, 1937-1947.   DOI
7 Sauerbrei, W. and Schumacher, M. (1992). A bootstrap resampling procedure for model building: Application to the Cox regression model. Statistical Medicine, 11, 2093-2099.   DOI
8 Tibshirani, R. (1997). The lasso method for variable selection in the Cox model. Statistics in Medicine, 16, 385-395.   DOI
9 Shim, J. and Seok, K. (2014). A transductive least squares support vector machine with the difference convex algorithm. Journal of the Korean Data & Information Science Society, 25, 455-464.   DOI
10 Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society B, 58, 267-288.
11 Zhou, M. (1992). M-estimation in censored linear models. Biometrika, 79, 837-841.   DOI
12 Bair, E. and Tibshirani, R. (2004). Semi-supervised methods to predict patient survival from gene expression data. PLoS Biology, 2, 511-522.
13 Buckley, J. and James, I. (1979). Linear regression with censored data. Biometrika, 66, 429-436.   DOI
14 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, OH, USA.
15 Cox, D. R. (1972) Regression models and life tables (with discussions). Journal of the Royal Statistical Society B, 74, 187-220.
16 Geyer, C. J. (1992). Practical Markov chain Monte Carlo (with discussion). Statistical Science, 7, 473-511.   DOI
17 Ghosh, K. S. and Ghosal, S. (2006). Semiparametric accelerated failure time models for censored data. Bayesian Statistics and Its Applications, 15, 213-229.
18 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, IA, USA.
19 Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of American Statistical Association, 53, 457-481.   DOI
20 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.