Asymmetric least squares regression estimation using weighted least squares support vector machine

  • Received : 2011.08.31
  • Accepted : 2011.09.21
  • Published : 2011.10.01

Abstract

This paper proposes a weighted least squares support vector machine for asymmetric least squares regression. This method achieves nonlinear prediction power, while making no assumption on the underlying probability distributions. The cross validation function is introduced to choose optimal hyperparameters in the procedure. Experimental results are then presented which indicate the performance of the proposed model.

Keywords

References

  1. Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions. Numerical Mathematics, 31, 377-403.
  2. Efron, B. (1991). Regression percentiles using asymmetric squared error loss. Statistica Sinica, 1, 93-125.
  3. Haerdle, W. (1989). Applied nonparametric regression, Cambridge University Press, New York.
  4. Hwang, C. (2010a). M-quantile regression using kernel machine technique. Journal of the Korean Data & Information Science Society, 21, 973-981.
  5. Hwang, C. (2010b). Support vector quantile regression for longitudinal data. Journal of the Korean Data & Information Science Society, 21, 309-316.
  6. 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.
  7. Newey, W. K. and Powell, J. L. (1987). Asymmetric least squares estimation and testing. Econometrica, 55, 819-847. https://doi.org/10.2307/1911031
  8. Schnabel, S. K. and Eilers, P. H. C. (2009). Optimal expectile smoothing. Computational Statistics and Data Analysis, 53, 4168-4177. https://doi.org/10.1016/j.csda.2009.05.002
  9. Seok, K. H. (2010). Semi-supervised classification with LS-SVM formulation. Journal of the Korean Data & Information Science Society, 21, 461-470.
  10. Shim, J. and Lee, J. T. (2009). Kernel method for autoregressive data. Journal of the Korean Data & Information Science Society, 20, 949-964.
  11. Shim, J., Seok, K. H. and Hwang, C. (2009). Non-crossing quantile regression via doubly penalized kernel machine. Computational Statistics, 24, 83-94. https://doi.org/10.1007/s00180-008-0123-y
  12. Suykens, J. A. K. and Vandewalle, J. (1999). Least squares support vector machine classifiers. Neural Processing Letters, 9, 293-300. https://doi.org/10.1023/A:1018628609742
  13. Taylor, J. W. (2008). Estimating value at risk and expected shortfall using expectiles. Journal of Financial Econometrics, 6, 231-252.
  14. Vapnik, V. (1995). The nature of statistical learning theory, Springer, New York.
  15. Yao, Q. and Tong, H. (1996). Asymmetric least squares regression estimation: A nonparametric approach. Journal of Nonparametric Statistics, 6, 273-292. https://doi.org/10.1080/10485259608832675