Periodic boxcar deconvolution and Diophantine approximation

DOI10.1214/009053604000000391zbMath1056.62044arXivmath/0503663OpenAlexW2000917920MaRDI QIDQ1766117

Iain M. Johnstone, Marc Raimondo

Publication date: 28 February 2005

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

Full work available at URL: https://arxiv.org/abs/math/0503663

zbMATH Keywords

rates of convergenceellipsoidill-posed problemdeconvolutioncontinued fractionlinear inverse problemminimax riskmotion blurirrational numberhyperrectangle

Mathematics Subject Classification ID

Random fields; image analysis (62M40) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Inference from stochastic processes (62M99) Numerical methods for inverse problems for integral equations (65R32) Diophantine approximation in probabilistic number theory (11K60)

Related Items

Adaptive sup-norm estimation of the Wigner function in noisy quantum homodyne tomography, Anisotropic de-noising in functional deconvolution model with dimension-free convergence rates, Wavelet deconvolution in a periodic setting with long-range dependent errors, Estimating the Upper Support Point in Deconvolution, Global uniform risk bounds for wavelet deconvolution estimators, Multichannel boxcar deconvolution with growing number of channels, Multichannel deconvolution with long-range dependence: a minimax study, Sharpness results concerning finite differences in Fourier analysis on the circle group, A SPECTRAL METHOD FOR DECONVOLVING A DENSITY, On convergence rates equivalency and sampling strategies in functional deconvolution models, Minimax and bayes estimation in deconvolution problem, Möbius deconvolution on the hyperbolic plane with application to impedance density estimation, Functional deconvolution in a periodic setting: uniform case, Density deconvolution under general assumptions on the distribution of measurement errors, Density deconvolution with non-standard error distributions: rates of convergence and adaptive estimation, Density estimation in the uniform deconvolution model, Simultaneous Wavelet Deconvolution in Periodic Setting, Multichannel deconvolution with long range dependence: upper bounds on the \(L^p\)-risk \((1 \leq p < \infty)\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal rates of convergence for nonparametric statistical inverse problems
• Minimax theory of image reconstruction
• Speed of estimation in positron emission tomography and related inverse problems
• Minimax risk over hyperrectangles, and implications
• Diophantine approximation
• Optimal filtering of square-integrable signals in Gaussian noise
• Linear integral equations.
• A statistical approach to some inverse problems for partial differential equations
• Oracle inequalities for inverse problems
• Sharp adaptation for inverse problems with random noise
• Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
• On minimax filtering over ellipsoids
• Optimal Discretization of Inverse Problems in Hilbert Scales. Regularization and Self-Regularization of Projection Methods
• Statistical Regularization of Inverse Problems
• Inverse problems as statistics
• Density estimation in the uniform deconvolution model
• Statistical Inverse Estimation in Hilbert Scales
• Wavelet Deconvolution in a Periodic Setting
• A statistical approach to the Cauchy problem for the Laplace equation
• Inverting noisy integral equations using wavelet expansions: a class of irregular convolutions