Bernoulli

  • Bernoulli
  • Volume 6, Number 4 (2000), 699-708.

Can adaptive estimators for Fourier series be of interest to wavelets?

Sam Efromovich

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Abstract

There is a firm belief in the literature on statistical applications of wavelets that adaptive procedures developed for Fourier series, labelled by that literature as `linear', are inadmissible because they are created for estimation of smooth functions and cannot attain optimal rates of mean integrated squared error convergence whenever an underlying function is spatially inhomogeneous, for instance, when it contains spikes/jumps and smooth parts. I use the recent remarkable results by Hall, Kerkyacharian and Picard on block-thresholded wavelet estimation to present a counterexample to that belief.

Article information

Source
Bernoulli, Volume 6, Number 4 (2000), 699-708.

Dates
First available in Project Euclid: 8 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1081449602

Mathematical Reviews number (MathSciNet)
MR2001h:62063

Zentralblatt MATH identifier
0980.62024

Keywords
Efromovich-Pinsker estimator filtering small sample sizes spatial adaptation

Citation

Efromovich, Sam. Can adaptive estimators for Fourier series be of interest to wavelets?. Bernoulli 6 (2000), no. 4, 699--708. https://projecteuclid.org/euclid.bj/1081449602


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References

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