Wavelet Nonparametric Regression Using Basis Averaging

  • Paul Yau
  • Robert Kohn
Part of the Lecture Notes in Statistics book series (LNS, volume 141)


Wavelet methods for nonparametric regression are fast and spatially adaptive. In particular, Bayesian methods are effective in wavelet estimation. Most wavelet methods use a particular basis to estimate the unknown regression function. In this chapter we use a Bayesian approach that averages over several different bases, and also over the Fourier basis, by weighting the estimate from each basis by the posterior probability of the basis. We show that estimators using basis averaging outperform estimators using a single basis and also estimators that first select the basis having the highest posterior probability and then estimate the unknown regression function using that basis.


Wavelet Base Basis Average Nonparametric Regression Marginal Likelihood Bayesian Estimator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Paul Yau
  • Robert Kohn

There are no affiliations available

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