Empirical risk minimization in inverse problems

DOI10.1214/09-AOS726zbMath1181.62044arXiv1001.2089MaRDI QIDQ847644

Jussi Klemelä, Enno Mammen

Publication date: 19 February 2010

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

Full work available at URL: https://arxiv.org/abs/1001.2089

zbMATH Keywords

Radon transformdeconvolutiontomographymultivariate density estimationempirical risk minimizationnonparametric function estimation

Mathematics Subject Classification ID

Density estimation (62G07) Estimation in multivariate analysis (62H12) Convergence of probability measures (60B10)

Related Items (5)

Noisy discriminant analysis with boundary assumptions ⋮ Empirical risk minimization in inverse problems ⋮ Adaptive sup-norm estimation of the Wigner function in noisy quantum homodyne tomography ⋮ Density estimation with minimization of \(U\)-divergence ⋮ Minimax fast rates for discriminant analysis with errors in variables

Cites Work

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• The existence and asymptotic properties of a backfitting projection algorithm under weak conditions
• A statistical perspective on ill-posed inverse problems (with discussion)
• Optimal rates of convergence for nonparametric statistical inverse problems
• Minimax theory of image reconstruction
• Empirical risk minimization in inverse problems
• Speed of estimation in positron emission tomography and related inverse problems
• On density estimation in the view of Kolmogorov's ideas in approximation theory
• Additive regression and other nonparametric models
• A central limit theorem under metric entropy with \(L_ 2\) bracketing
• Renormalization exponents and optimal pointwise rates of convergence
• Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes
• Rates of convergence for minimum contrast estimators
• Information-theoretic determination of minimax rates of convergence
• Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
• Optimal rates of convergence of estimates in the stochastic problem of computerized tomography
• Convergence of estimates under dimensionality restrictions
• Penalized contrast estimator for adaptive density deconvolution
• The cross-validated adaptive epsilon-net estimator
• Law of the iterated logarithm for set-indexed partial sum processes with finite variance
• Uniform Central Limit Theorems
• Estimation of Multivariate Regression
• On the representation of continuous functions of several variables by superpositions of continuous functions of a smaller number of variables
• PIECEWISE-POLYNOMIAL APPROXIMATIONS OF FUNCTIONS OF THE CLASSES $ W_{p}^{\alpha}$
• Minimax estimation of the solution of an ill-posed convolution type problem

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