Bayesian wavelet shrinkage for nonparametric mixed-effects models

Su Yun Huang*, Henry Horng Shing Lu

*Corresponding author for this work

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

The main purpose of this article is to study the wavelet shrinkage method from a Bayesian viewpoint. Nonparametric mixed-effects models are proposed and used for interpretation of the Bayesian structure. Bayes and empirical Bayes estimation are discussed. The latter is shown to have the Gauss-Markov type optimality (i.e., BLUP), to be equivalent to a method of regularization estimator (MORE), and to be minimax in a certain class. Characterization of prior and posterior regularity is discussed. The smoothness of posterior estimators is controlled via prior parameters. Computational issues including the use of generalized cross validation are discussed, and examples are presented.

Original languageEnglish
Pages (from-to)1021-1040
Number of pages20
JournalStatistica Sinica
Volume10
Issue number4
StatePublished - 1 Oct 2000

Keywords

  • Bayesian regression
  • Besov spaces
  • Best linear unbiased prediction (BLUP)
  • Gauss-Markov estimation
  • Generalized cross validation
  • Non-parametric regression
  • Sobolev regularization
  • Wavelet shrinkage

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