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Efficient resolution and basis functions selection in wavelet regression

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  • Chun Park
  • Inyoung Kim

Abstract

In this paper we propose an efficient method to determine a primary resolution and wavelet basis functions in wavelet regression. Most wavelet shrinkage methods focus on thresholding the wavelet coefficients, given a primary resolution which is usually determined by the sample size. However, both a primary resolution and the basis functions are affected by the shape of an unknown function rather than the sample size. Unlike existing methods, our method takes the shape of the unknown function into account because a proper resolution can be much affected by the shape of it rather than the sample size. Our approach to determine a primary resolution and wavelet basis functions is developed under Bayesian framework using the posterior model probability. We demonstrate the advantage of our approach using a simulation study and a real data application. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Chun Park & Inyoung Kim, 2015. "Efficient resolution and basis functions selection in wavelet regression," Computational Statistics, Springer, vol. 30(4), pages 957-986, December.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:4:p:957-986
    DOI: 10.1007/s00180-015-0575-9
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    References listed on IDEAS

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    1. Antoniadis A. & Fan J., 2001. "Regularization of Wavelet Approximations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 939-967, September.
    2. Chun Park & Hee-Seok Oh & Hakbae Lee, 2008. "Bayesian selection of primary resolution and wavelet basis functions for wavelet regression," Computational Statistics, Springer, vol. 23(2), pages 291-302, April.
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