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Nonlinear regression modeling via regularized wavelets and smoothing parameter selection

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  • Fujii, Toru
  • Konishi, Sadanori

Abstract

We introduce regularized wavelet-based methods for nonlinear regression modeling when design points are not equally spaced. A crucial issue in the model building process is a choice of tuning parameters that control the smoothness of a fitted curve. We derive model selection criteria from an information-theoretic and also Bayesian approaches. Monte Carlo simulations are conducted to examine the performance of the proposed wavelet-based modeling technique.

Suggested Citation

  • Fujii, Toru & Konishi, Sadanori, 2006. "Nonlinear regression modeling via regularized wavelets and smoothing parameter selection," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 2023-2033, October.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:9:p:2023-2033
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    References listed on IDEAS

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    1. Antoniadis, Anestis & Dinh Tuan Pham, 1998. "Wavelet regression for random or irregular design," Computational Statistics & Data Analysis, Elsevier, vol. 28(4), pages 353-369, October.
    2. Sadanori Konishi, 2004. "Bayesian information criteria and smoothing parameter selection in radial basis function networks," Biometrika, Biometrika Trust, vol. 91(1), pages 27-43, March.
    3. Marianna Pensky & Brani Vidakovic, 2001. "On Non-Equally Spaced Wavelet Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 681-690, December.
    4. Antoniadis A. & Fan J., 2001. "Regularization of Wavelet Approximations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 939-967, September.
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    Cited by:

    1. Hidetoshi Matsui & Takamitsu Araki & Sadanori Konishi, 2011. "Multiclass Functional Discriminant Analysis and Its Application to Gesture Recognition," Journal of Classification, Springer;The Classification Society, vol. 28(2), pages 227-243, July.

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