On loss functions for model selection in wavelet based Bayesian method

  • Park, Chun-Gun (Department of Applied Statistics, Konkuk University)
  • Published : 2009.11.30

Abstract

Most Bayesian approaches to model selection of wavelet analysis have drawbacks that computational cost is expensive to obtain accuracy for the fitted unknown function. To overcome the drawback, this article introduces loss functions which are criteria for level dependent threshold selection in wavelet based Bayesian methods with arbitrary size and regular design points. We demonstrate the utility of these criteria by four test functions and real data.

Keywords

References

  1. Abramovich, F., Besbeas, P. and Sapatinas, T. (2002). Empirical Bayes approach to block wavelet function estimation. Computational Statistics and Data Analysis, 39, 435-451. https://doi.org/10.1016/S0167-9473(01)00085-8
  2. Antoniadis, A. and Sapatinas, T. (2001). Wavelet shrinkage for natural exponential families with quadratic variance functions. Biometrika, 88, 805-820. https://doi.org/10.1093/biomet/88.3.805
  3. Daubechies, I. (1992). Ten lectures on wavelets, CBMS-NSF, Series in Applied Mathematics, No. 61, SIAM, Philadelphia.
  4. Misiti, M., Misiti, Y., Oppenheim, G. and Poggi, J. M. (1994). Wavelet toolbox for use with MATLAB, The Math Works Incorporation.
  5. Park, C. G. (2008). A note on a Bayesian approach to the choice of wavelet basis functions at each resolution level. Journal of Korean Data & Information Science Society, 19, 1465-1476.
  6. Park, C. G., Hart, Jeffrey D., Vannucci, M. (2005). Bayesian methods for wavelet series in single-index models. Journal of Computational and Graphical Statistics, 14, 770-794. https://doi.org/10.1198/106186005X79007
  7. Park, C. G., Kim, Y. H. and Yang, W. Y. (2004). Determinacy on a maximum resolution in wavelet series. Journal of Korean Data & Information Science Society, 15, 467-476.
  8. Park, C. G., Oh, H. S. and Lee, H. B. (2008). Bayesian selection of primary resolution and wavelet basis functions for wavelet regression. Computational Statistics, 23, 291-302.
  9. Wang, X. and Wood, Andrew, T. A. (2006). Empirical Bayes block shrinkage of wavelet coefficients via the noncentral $X^{2}$ distribution. Biometrika, 93, 705-722. https://doi.org/10.1093/biomet/93.3.705