Empirical Bayes approach to wavelet regression using $\epsilon$-contaminated priors (Articolo in rivista)

  • Empirical Bayes approach to wavelet regression using $\epsilon$-contaminated priors (Articolo in rivista) (literal)
  • 2004-01-01T00:00:00+01:00 (literal)
Alternative label
  • Angelini C., Sapatinas T. (2004)
    Empirical Bayes approach to wavelet regression using $\epsilon$-contaminated priors
    in Journal of statistical computation and simulation (Print)
  • Angelini C., Sapatinas T. (literal)
Pagina inizio
  • 741 (literal)
Pagina fine
  • 764 (literal)
  • 74 (literal)
  • ISI Web of Science (WOS) (literal)
  • Thoefanis Sapatinas, Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, CY 1678 Nicosia, Cyprus (literal)
  • Empirical Bayes approach to wavelet regression using $\epsilon$-contaminated priors (literal)
  • We consider an empirical Bayes approach to standard nonparametric regression estimation using a nonlinear wavelet methodology. Instead of specifying a single prior distribution on the parameter space of wavelet coefficients, that is usually the case in the existing literature, we elicit the $\epsilon$-contamination class of prior distributions that is particularly attractive to work with when one seeks robust priors in Bayesian analysis. The type II maximum likelihood approach to prior selection is used by maximizing the predictive distribution for the data in the wavelet domain over a suitable subclass of the $\epsilon$-contamination class of prior distributions. For the prior selected, the posterior mean yields a thresholding procedure which depends on one free prior parameter and it is level - and amplitude- dependent, allowing thus for better adaptation in function estimation. We consider an automatic choice of the free prior parameter, guided by considerations on an exact risk analysis and on the shape of the thresholding rule, enabling the resulting estimator to be fully automated in practice. We also compute pointwise Bayesian credible intervals for the resulting function estimate using a simulation-based approach. We use several simulated examples to illustrate the performance of the proposed empirical Bayes term-by-term wavelet scheme, and we make comparisons with other classical and empirical Bayes term-by-term wavelet schemes. As a practical illustration, we present an application to a real-life data set that was collected in an atomic force microscopy study. (literal)
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