Empirical Bayes oracle uncertainty quantification for regression

DOI10.1214/19-AOS1845zbMath1461.62120OpenAlexW3112375583MaRDI QIDQ1996760

Eduard Belitser, Subhashis Ghosal

Publication date: 26 February 2021

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aos/1607677229

zbMATH Keywords

empirical Bayescoverageoracle ratecredible ballexcessive bias restriction

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Linear regression; mixed models (62J05) Nonparametric tolerance and confidence regions (62G15) Empirical decision procedures; empirical Bayes procedures (62C12)

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Cites Work

• Unnamed Item
• Empirical Bayes posterior concentration in sparse high-dimensional linear models
• Supremum norm posterior contraction and credible sets for nonparametric multivariate regression
• Statistical significance in high-dimensional linear models
• Nonparametric Bernstein-von Mises theorems in Gaussian white noise
• On the Bernstein-von Mises phenomenon for nonparametric Bayes procedures
• Bayesian inverse problems with Gaussian priors
• Adaptive Bernstein-von Mises theorems in Gaussian white noise
• An analysis of Bayesian inference for nonparametric regression
• Component selection and smoothing in multivariate nonparametric regression
• Bayesian linear regression with sparse priors
• Adaptive Bayesian credible sets in regression with a Gaussian process prior
• Credible sets in the fixed design model with Brownian motion prior
• High-dimensional additive modeling
• On the Bernstein-von Mises theorem with infinite-dimensional parameters
• Fast Bayesian model assessment for nonparametric additive regression
• An adaptation theory for nonparametric confidence intervals
• Honest confidence regions for nonparametric regression
• Adaptive confidence interval for pointwise curve estimation.
• Confidence balls in Gaussian regression.
• On the conditions used to prove oracle results for the Lasso
• Confidence intervals for high-dimensional linear regression: minimax rates and adaptivity
• On coverage and local radial rates of credible sets
• Spike and slab empirical Bayes sparse credible sets
• Needles and straw in a haystack: robust confidence for possibly sparse sequences
• Minimax-optimal nonparametric regression in high dimensions
• Confidence sets in sparse regression
• Frequentist coverage of adaptive nonparametric Bayesian credible sets
• Ideal spatial adaptation by wavelet shrinkage
• Sparse Additive Models
• Minimax-optimal rates for sparse additive models over kernel classes via convex programming
• Fundamentals of Nonparametric Bayesian Inference
• Gaussian model selection

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