Numerical performance of block thresholded wavelet estimators

  • Authors:

  • Peter Hall;Spiridon Penev;Gérard Kerkyacharian;Dominique Picard

  • Affiliations:

  • Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia;School of Mathematics, University of NSW, Sydney, NSW 2052, Australia;Faculté Mathematiques et Informatiques, Université de Picardie, 33 rue Saint-Leu, 80039 Amiens Cedex 01, France;De´partement de Mathematiques, Universite´ de Paris VII Paris Cedex 05, France

  • Venue:
  • Statistics and Computing
  • Year:
  • 1997

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Abstract

Usually, methods for thresholding wavelet estimators are implemented term by term, with empirical coefficients included or excluded depending on whether their absolute values exceed a level that reflects plausible moderate deviations of the noise. We argue that performance may be improved by pooling coefficients into groups and thresholding them together. This procedure exploits the information that coefficients convey about the sizes of their neighbours. In the present paper we show that in the context of moderate to low signal-to-noise ratios, this ’block thresholding‘ approach does indeed improve performance, by allowing greater adaptivity and reducing mean squared error. Block thresholded estimators are less biased than term-by-term thresholded ones, and so react more rapidly to sudden changes in the frequency of the underlying signal. They also suffer less from spurious aberrations of Gibbs type, produced by excessive bias. On the other hand, they are more susceptible to spurious features produced by noise, and are more sensitive to selection of the truncation parameter.