Empirical Bayes scaling of Gaussian priors in the white noise model

DOI10.1214/13-EJS798zbMath1336.62039OpenAlexW2081386230MaRDI QIDQ1951145

J. H. van Zanten, B. T. Szabó, Aad W. van der Vaart

Publication date: 29 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ejs/1366031048

zbMATH Keywords

bandwidthGaussian white noiseadaptationrate of contractionnormal means modelhyper-rectangle

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Bayesian inference (62F15) Nonparametric tolerance and confidence regions (62G15) Empirical decision procedures; empirical Bayes procedures (62C12)

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Uses Software

• EBayesThresh

Cites Work

• Bayes procedures for adaptive inference in inverse problems for the white noise model
• Bayesian inverse problems with Gaussian priors
• An analysis of Bayesian inference for nonparametric regression
• Adaptive Bayesian estimation using a Gaussian random field with inverse gamma bandwidth
• Minimax risk over hyperrectangles, and implications
• Rates of contraction of posterior distributions based on Gaussian process priors
• Empirical Bayesian test of the smoothness
• Optimal filtering of square-integrable signals in Gaussian noise
• Statistical estimation and optimal recovery
• Adaptive Bayesian inference on the mean of an infinite-dimensional normal distribution
• On the Bernstein-von Mises theorem with infinite-dimensional parameters
• General empirical Bayes wavelet methods and exactly adaptive minimax estimation
• Convergence rates of posterior distributions.
• Bayesian aspects of some nonparametric problems
• Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences
• Weak convergence and empirical processes. With applications to statistics
• Lower bounds for posterior rates with Gaussian process priors
• Convergence rates for Bayesian density estimation of infinite-dimensional exponential families
• General maximum likelihood empirical Bayes estimation of normal means
• Bayesian inference with rescaled Gaussian process priors
• Nonparametric Bayesian model selection and averaging
• Regularized Posteriors in Linear Ill-Posed Inverse Problems
• Sharp adaptive estimation by a blockwise method
• On universal Bayesian adaptation
• Limiting the Risk of Bayes and Empirical Bayes Estimators--Part II: The Empirical Bayes Case
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