Abstract
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.
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© 1999 Springer Science+Business Media New York
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Yau, P., Kohn, R. (1999). Wavelet Nonparametric Regression Using Basis Averaging. In: Müller, P., Vidakovic, B. (eds) Bayesian Inference in Wavelet-Based Models. Lecture Notes in Statistics, vol 141. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0567-8_7
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DOI: https://doi.org/10.1007/978-1-4612-0567-8_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98885-6
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