Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Estimating Variance Function with Kernel Machine

  • Published : 2009.03.30

Abstract

In this paper we propose a variance function estimation method based on kernel trick for replicated data or data consisted of sample variances. Newton-Raphson method is used to obtain associated parameter vector. Furthermore, the generalized approximate cross validation function is introduced to select the hyper-parameters which affect the performance of the proposed variance function estimation method. Experimental results are then presented which illustrate the performance of the proposed procedure.

Keywords

File

Download PDF

References

  1. Anderson, T. G. and Lund, J. (1997). Estimating continuous-time stochastic volatility models of the short-term interest rate, Journal of Econometrics, 77, 343-377 https://doi.org/10.1016/S0304-4076(96)01819-2
  2. Friedman, J. H. (1991). Multivariate adaptive regression splines, The Annals of Statistics, 19, 1-67 https://doi.org/10.1214/aos/1176347963
  3. Green, P. J. and Silverman, B. W. (1994). Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman & Hall/CRC, London
  4. Hall, P. and Carroll, R. J. (1989). Variance function estimation in regression: The effect of estimating the mean, Journal of the Royal Statistical Society, Series B, 51, 3-14
  5. 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
  6. 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
  7. Mercer, J. (1909). Functions of positive and negative type and their connection with the theory of integral equations, Philosophical Transactions of Royal Society of London, Serise A, 209, 415-446 https://doi.org/10.1098/rsta.1909.0016
  8. Vapnik, V. N. (1995). The Nature of Statistical Learning Theory, Springer, New York
  9. Wei, Y., Pere, A., Koenker, R. and He, X. (2006). Quantile regression methods for reference growth charts, Statistics in Medicine, 25, 1369-1382 https://doi.org/10.1002/sim.2271
  10. Xiang, D. and Wahba, G. (1996). A generalized approximate cross validation for smoothing splines with non-Gaussian data, Statistian Sinica, 6, 675-692