Wavelet Nonparametric Regression Using Basis Averaging
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.
KeywordsWavelet Base Basis Average Nonparametric Regression Marginal Likelihood Bayesian Estimator
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- Clyde, M. Parmigiani, G. and Vidakovic, B. (1997). Multiple shrinkage and subset selection in wavelets. Biometrika, 391-402.Google Scholar
- George, E. I. and Foster, D. (1997). Calibration and empirical Bayes variable selection. Preprint.Google Scholar
- Kohn, R., Marron, J. S. and Yau, P. (1997) Wavelet estimation using basis selection and basis averaging. Preprint.Google Scholar
- Marron, J. S., Adak, S., Johnstone, I. M., Neumann, M. and Patil, P. (1998) Exact risk analysis of wavelet regression. Journal of Computational and Graphical Statistics, 278-309.Google Scholar