References
- Basset, G. and Koenker, R. (1982). An empirical quantile function for linear models with iid errors. Journal of the American Statistical Association, 77, 407-415. https://doi.org/10.2307/2287261
- He, X. (1997). Quantile curves without crossing. The American Statistician, 51, 186-192. https://doi.org/10.2307/2685417
- Heagerty, P. J. and Pepe, M. S. (1999). Semiparametric estimation of regression quantiles with application to standardizing weight for height and age in US children. Applied Statistics, 48, 533-551.
- Hwang, C. and Shim, J. (2005). A simple quantile regression via support vector machine. Lecture Notes in Computer Science, 3610, 512-520.
- Kimeldorf, G. S. and Wahba, G. (1971). Some results on Tchebycheffian spline functions. Journal of Mathematical Analysis and its Applications, 33, 82-95. https://doi.org/10.1016/0022-247X(71)90184-3
- Koenker, R. (2005). Quantile regression, Cambridge University Press, London.
- Koenker, R. and Bassett, G. (1978). Regression quantiles. Econometrica, 46, 33-50. https://doi.org/10.2307/1913643
- Mercer, J. (1909). Functions of positive and negative and their connection with the theory of integral equations. Philosphical Transactions of the Royal Society, A, 415-446.
- Powell, J. L. (1986). Censored regression quantiles. Journal of Econometrics, 32, 143-155. https://doi.org/10.1016/0304-4076(86)90016-3
- Shim, J., Hwang, C. and Seok, K. (2009). Non-crossing quantile regression via doubly penalized kernel machine. Computational Statistics, 24, 83-94. https://doi.org/10.1007/s00180-008-0123-y
- Shim, J., Park, H. and Hwang, C. (2009). A kernel machine for estimation of mean and volatility functions. Journal of the Korean Data & Information Science Society, 20, 905-912.
- Shim, J., Park, H. and Seok, K. (2009). Variance function estimation with LS-SVM for replicated data. Journal of the Korean Data & Information Science Society, 20, 925-931.
- Smola, A. J. and Scholkopf, B. (1998). A tutorial on support vector regression. NeuroCOLT2 Technical Report, NeuroCOLT.
- Sohn, I., Kim, S., Hwang, C., Lee, J. W. and Shim, J. (2008). Support vector machine quantile regression for detecting differentially expressed genes in microarray analysis. Methods of Information in Medicine, 47, 459-467.
- Vapnik, V. N. (1998). Statistical learning theory, Springer.
- Weiss, A. (1991). Estimating nonlinear dynamic models using least absolute error estimation. Econometric Theory, 7, 46-68. https://doi.org/10.1017/S0266466600004230
- White, H. (1992). Nonparametric estimation of conditional quantile using neural networks, in H. White, eds., Artificial Neural Networks: Approximation and Learning Theory, Blackwell, Oxford, 191-205.
- Xiang, D. and Wahba, G. (1996). A generalized approximate cross validation for smoothing splines with non-Gaussian data. Statistica Sinica, 6, 675-692.
- Yuan, M. and Wahba, G. (2004). Doubly penalized likelihood estimator in heteroscedastic regression. Statistics and Probability Letter , 69, 11-20.