This paper deals with the estimations of the least squares support vector regression when the responses are subject to randomly right censoring. The estimation is performed via two steps - the ordinary least squares support vector regression and the least squares support vector regression with censored data. We use the empirical fact that the estimated regression functions subject to randomly right censoring are close to the true regression functions than the observed failure times subject to randomly right censoring. The hyper-parameters of model which affect the performance of the proposed procedure are selected by a generalized cross validation function. Experimental results are then presented which indicate the performance of the proposed procedure.
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.
Gunn, S. R. (1998). Support vector machines for classication and regression, Technical report, Department of Electronics and Computer Science, Southamption, England, United Kingdom.
Heuchenne, C. and Van Keilegom, I. (2005). Nonlinear regression with censored data, Technometrics, 49, 34-44.
Hwang, C. and Shim, J. (2010). Semiparametric support vector machine for accelerated failure time model. Journal of the Korean Data & Information Science Society, 21, 467-477.
Jin, Z., Lin, D. Y., Wei, L. J. and Ying, Z. L. (2003). Rank-based inference for the accelerated failure time model. Biometrika, 90, 341-353.
Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457-481.
Kimeldorf, G. and Wahba, G. (1981). Some results on Tchebychean spline functions. Journal of Mathematical Analysis and Applications, 33, 82-95.
Koul, H., Susarla, V. and Van Ryzin J. (1981). Regression analysis with randomly right censored data. The Annal of Statistics, 9, 1276-1288.
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.
Miller, R. G. (1976). Least squares regression with censored data. Biometrika, 63, 449-464.
Shim, J., Kim, C. R. and Hwang, C. (2011). Semiparametric least squares support vector machine for accelerated failure time model. Journal of the Korean Statistical Society, 40, 75-83.
Shim, J. (2005). Censored kernel ridge regression. Journal of the Korean Data & Information Science Society, 16, 1045-1052.
Shim, J. and Lee, J. T. (2009). Kernel method for autoregressive data. Journal of the Korean Data & Information Science Society, 20, 467-4720.
Smola, A. and Scholkopf, B. (1998). On a kernel-based method for pattern recognition, regression, approximation and operator inversion. Algorithmica, 22, 211-231.
Stute, W. (1993). Consistent estimation under random censorship when covariables are available. Journal of Multivariate Analysis, 45, 89=103.
Suykens, J. A. K. and Vanderwalle, J. (1999). Least square support vector machine classifier. Neural Processing Letters, 9, 293-300.
Vapnik, V. N. (1998). Statistical learning theory, Wiley, New York.
Yang, S. (1999). Censored median regression using weighted empirical survival and hazard functions. Journal of the American Statistical Association, 94, 137-145.
Ying, Z. L., Jung, S. H. and Wei, L. J. (1995). Survival analysis with median regression models, Journal of the American Statistical Association, 90, 178-184.
Zhou, M. (1992). M-estimation in censored linear models. Biometrika, 79, 837-841.
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2013. "" Journal of the Korean Data & Information Science Society = 한국데이터정보과학회지, 24(3): 625~636