EbayesThresh: Empirical Bayes Thresholding and Related Methods. This package carries out Empirical Bayes thresholding using the methods developed by I. M. Johnstone and B. W. Silverman. The basic problem is to estimate a mean vector given a vector of observations of the mean vector plus white noise, taking advantage of possible sparsity in the mean vector. Within a Bayesian formulation, the elements of the mean vector are modelled as having, independently, a distribution that is a mixture of an atom of probability at zero and a suitable heavy-tailed distribution. The mixing parameter can be estimated by a marginal maximum likelihood approach. This leads to an adaptive thresholding approach on the original data. Extensions of the basic method, in particular to wavelet thresholding, are also implemented within the package.
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References in zbMATH (referenced in 8 articles )
Showing results 1 to 8 of 8.
- Park, Junyong: Shrinkage estimator in normal mean vector estimation based on conditional maximum likelihood estimators (2014)
- Frommlet, Florian; Bogdan, Małgorzata: Some optimality properties of FDR controlling rules under sparsity (2013)
- Wolpert, Robert L.; Clyde, Merlise A.; Tu, Chong: Stochastic expansions using continuous dictionaries: Lévy adaptive regression kernels (2011)
- Zhang, Dabao; Lin, Yanzhu; Zhang, Min: Penalized orthogonal-components regression for large $p$ small $n$ data (2009)
- Fryzlewicz, Piotr: Data-driven wavelet-Fisz methodology for nonparametric function estimation (2008)
- Braak, Cajo J.F.Ter: Bayesian sigmoid shrinkage with improper variance priors and an application to wavelet denoising (2006)
- Johnstone, Iain M.; Silverman, Bernard W.: Empirical Bayes selection of wavelet thresholds (2005)
- Johnstone, Iain M.; Silverman, Bernhard W.: Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences (2004)