Nonlinear estimation over weak Besov spaces and minimax Bayes

DOI10.3150/bj/1155735929zbMath1125.62001OpenAlexW2037248027MaRDI QIDQ850765

Vincent Rivoirard

Publication date: 6 November 2006

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3150/bj/1155735929

zbMATH Keywords

rate of convergenceminimax riskwhite noise modelBayes methodasymptotically least favourable priorsthresholding rulesweak Besov spaces

Mathematics Subject Classification ID

Bayesian inference (62F15) Bayesian problems; characterization of Bayes procedures (62C10) Minimax procedures in statistical decision theory (62C20) Inference from stochastic processes (62M99) Applications of functional analysis in probability theory and statistics (46N30)

Related Items (7)

Thresholding procedure with priors based on Pareto distributions ⋮ Adaptive tests of homogeneity for a Poisson process ⋮ Sparse regression learning by aggregation and Langevin Monte-Carlo ⋮ The Lasso as an \(\ell _{1}\)-ball model selection procedure ⋮ Mirror averaging with sparsity priors ⋮ Hyperbolic wavelet thresholding methods and the curse of dimensionality through the maxiset approach ⋮ Spaces of Besov-Sobolev type and a problem on nonlinear approximation

Cites Work

• The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality
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• Neo-classical minimax problems, thresholding and adaptive function estimation
• Restricted nonlinear approximation
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• Unconditional bases and bit-level compression
• Nonlinear Wavelet Shrinkage with Bayes Rules and Bayes Factors
• Ten Lectures on Wavelets
• Wavelet Thresholding via A Bayesian Approach
• Ideal spatial adaptation by wavelet shrinkage
• Maximal spaces with given rate of convergence for thresholding algorithms
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