Minimax Bayes, Asymptotic Minimax and Sparse Wavelet Priors

By Iain M. Johnstone. 1994

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Citations in the corpus

Minimax estimation via wavelet shrinkage (1998, methodology): “Ž .separate article Donoho and Johnstone 1994a hereafter DJ94a we develop a theory of ideal spatial adaptation, relate it to efforts mentioned above and show that, when properly tuned, nonlinear wavelet shrinkage provides near-ideal spatial adaptation.”
Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study (2001, background): “Some key words: EM ALGORITHM; EMPIRICAL BAYES; MONTE CARLO EXPERIMENTS; NONPARAMETRIC REGRESSION; SMOOTHING METHODS; SHRINKAGE; THRESHOLDING; WAVELETS.”
Posterior concentration rates for infinite dimensional exponential families (2012, methodology): “Such phenomena have been investigated using various approaches: in the minimax approach by Donoho et al. [7] or Reynaud-Bouret et al. [16] and in the Bayesian context where least favorable priors for such spaces are built (see Johnstone [12] or Rivoirard [17]).”
General maximum likelihood empirical Bayes estimation of normal means (2009, background): “A minimax theory for (weak) lp balls uniform in (p,C) can be developed by careful combination and improvement of the proofs in [12, 23, 38].”
Near optimal thresholding estimation of a Poisson intensity on the real line (2008, methodology): “They constitute a useful tool to classify wavelet decomposed signals with respect to their regularity and sparsity properties (see [28]).”
On optimality of Bayesian testimation in the normal means problem (2007, unknown): “6793. https://stars.library.ucf.edu/facultybib2000/6793 The Annals of Statistics 2007, Vol. 35, No. 5, 2261–2286 DOI: 10.1214/009053607000000226 © Institute of Mathematical Statistics, 2007”