Bayesian selection of primary resolution and wavelet basis functions for wavelet regression

Chun Gun Park, Hee Seok Oh, Hakbae Lee

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Abstract

This paper considers a Bayesian approach to selecting a primary resolution and wavelet basis functions. Most of papers on wavelet shrinkage have been focused on thresholding of wavelet coefficients, given a primary resolution which is usually determined by the sample size. However, it turns out that a proper primary resolution is much affected by the shape of an unknown function rather than by the sample size. In particular, Bayesian approaches to wavelet series suffer from computational burdens if the chosen primary resolution is too high. A surplus primary resolution may result in a poor estimate. In this paper, we propose a simple Bayesian method to determine a primary resolution and wavelet basis functions independently of the sample size. Results from a simulation study demonstrate the promising empirical properties of the proposed approach.

Original languageEnglish
Pages (from-to)291-302
Number of pages12
JournalComputational Statistics
Volume23
Issue number2
DOIs
Publication statusPublished - 2008 Apr 1

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Mathematics

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