Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지

Doubly penalized kernel method for heteroscedastic autoregressive datay

  • Cho, Dae-Hyeon (Department of Data Science, Institute of Statistical Information, Inje University) ;
  • Shim, Joo-Yong (Department of Applied Statistics, Catholic University of Daegu) ;
  • Seok, Kyung-Ha (Department of Data Science, Institute of Statistical Information, Inje University)
  • Published : 2010.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we propose a doubly penalized kernel method which estimates both the mean function and the variance function simultaneously by kernel machines for heteroscedastic autoregressive data. We also present the model selection method which employs the cross validation techniques for choosing the hyper-parameters which aect the performance of proposed method. Simulated examples are provided to indicate the usefulness of proposed method for the estimation of mean and variance functions.

Keywords

References

  1. Aizerman, M. A., Braverman, E. M. and Rozonoer, L. I. (1964). Theoretical foundation of potential function method in pattern recognition learning. Automation and Remote Control, 25, 821-837.
  2. Anderson, T. G. and Lund, J. (1997). Estimating continuous-time stochastic volatility models of short-term interest rate. Journal of Econometrics, 77, 343-377. https://doi.org/10.1016/S0304-4076(96)01819-2
  3. Fan, J. Q. and Yao, Q. W. (1998). Efficient estimation of conditional variance functions in stochastic regression. Biometrika, 85, 645-660. https://doi.org/10.1093/biomet/85.3.645
  4. Golub, G. H., Heath, M. and Wahba, G. (1979). Generalized cross validation as a method for choosing a good ridge parameter. Technometrics, 21, 215-223. https://doi.org/10.2307/1268518
  5. Hwang, C. (2008). Mixed effects kernel binomial regression. Journal of Korean Data & Information Science Society, 19, 1327-1334.
  6. Juditsky, A, Hjalmarsson, H., Benveniste, A., Deylon, B., Ljung, L., Sj o. berg, J. and Zhang, Q. (1995). Nonlinear black-box modelling in system identification: Mathematical foundations. Automatica, 31, 1725-1750. https://doi.org/10.1016/0005-1098(95)00119-1
  7. 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
  8. Liu, A., Tong, T. and Wang, Y. (2007). Smoothing spline estimation of variance functions. Journal of Computational and Graphical Statistics, 16, 312-329. https://doi.org/10.1198/106186007X204528
  9. 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. https://doi.org/10.1098/rsta.1909.0016
  10. Ruppert, D., Wand, M. P., Holst, U. and Hossjer, O. (1997). Local polynomial variance-function estimation. Technometrics, 39, 262-73. https://doi.org/10.2307/1271131
  11. Shim, J. and Lee, J. T. (2009). Kernel method for autoregressive data. Journal of Korean Data and Information Science Society, 20, 949-954.
  12. Shim, J., Park, H. J. and Seok, K. H. (2008). Kernel Poisson regression for longitudinal data. Journal of Korean Data & Information Science Society, 19, 1353-1360.
  13. Shim, J., Park, H. J. and Seok, K. H. (2009). Variance function estimation with LS-SVM for replicated data. Journal of Korean Data and Information Science Society, 20, 925-931.
  14. Suykens, J. A. K. and Vanderwalle, J. (1999). Least square support vector machine classifier. Neural Processing Letters, 9, 293-300. https://doi.org/10.1023/A:1018628609742
  15. Xiang, D. and Wahba, G. (1996). A generalized approximate cross validation for smoothing splines with non-gaussian data. Statistian Sinica, 6, 675-692.
  16. Yuan, M. and Wahba, G. (2004). Doubly penalized likelihood estimator in heteroscedastic regression. Statistics & Probability Letters, 69, 11-20. https://doi.org/10.1016/j.spl.2004.03.009