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The Stationary Wavelet Transform and some Statistical Applications

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Wavelets and Statistics

Part of the book series: Lecture Notes in Statistics ((LNS,volume 103))

Abstract

Wavelets are of wide potential use in statistical contexts. The basics of the discrete wavelet transform are reviewed using a filter notation that is useful subsequently in the paper. A ‘stationary wavelet transform’, where the coefficient sequences are not decimated at each stage, is described. Two different approaches to the construction of an inverse of the stationary wavelet transform are set out. The application of the stationary wavelet transform as an exploratory statistical method is discussed, together with its potential use in nonparametric regression. A method of local spectral density estimation is developed. This involves extensions to the wavelet context of standard time series ideas such as the periodogram and spectrum. The technique is illustrated by its application to data sets from astronomy and veterinary anatomy.

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Authors and Affiliations

  1. Department of Mathematics, University of Bristol, BS8 1TW, Bristol, UK

    G. P. Nason & B. W. Silverman

Authors
  1. G. P. Nason
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  2. B. W. Silverman
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Editor information

Editors and Affiliations

  1. Laboratoire IMAG-LMC, University Joseph Fourier, F-38402, Grenoble Cedex, France

    Anestis Antoniadis

  2. Laboratoire MSS, University Paris-Sud, F-92405, Orsay Cedex, France

    Georges Oppenheim

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© 1995 Springer-Verlag New York

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Nason, G.P., Silverman, B.W. (1995). The Stationary Wavelet Transform and some Statistical Applications. In: Antoniadis, A., Oppenheim, G. (eds) Wavelets and Statistics. Lecture Notes in Statistics, vol 103. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2544-7_17

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  • DOI: https://doi.org/10.1007/978-1-4612-2544-7_17

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94564-4

  • Online ISBN: 978-1-4612-2544-7

  • eBook Packages: Springer Book Archive

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