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Variational multiscale nonparametric regression: smooth functions (Q1650131)

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Language	Label	Description	Also known as
English	Variational multiscale nonparametric regression: smooth functions	scientific article

Statements

scholarly article

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Variational multiscale nonparametric regression: smooth functions (English)

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Markus Grasmair

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Annales de l'Institut Henri Poincaré. Probabilités et Statistiques

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publication date

29 June 2018

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full work available at URL

https://arxiv.org/abs/1512.01068

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https://projecteuclid.org/euclid.aihp/1524643240

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zbMATH Keywords

nonparametric regression

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adaptation

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convergence rates

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minimax optimality

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multiresolution norm

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approximate source conditions

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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A general form of the covering principle and relative differentiation of additive functions

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A general form of the covering principle and relative differentiation of additive functions. II

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Simultaneous analysis of Lasso and Dantzig selector

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Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications

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The Mathematical Theory of Finite Element Methods

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Stable Recovery of Sparse Signals and an Oracle Inequality

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A data-driven block thresholding approach to wavelet estimation

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New multiscale transforms, minimum total variation synthesis: Applications to edge-preserving image reconstruction

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The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).

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Oracle inequalities for inverse problems

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A first-order primal-dual algorithm for convex problems with applications to imaging

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Detection with the scan and the average likelihood ratio

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Image Processing and Analysis

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Stein block thresholding for wavelet-based image deconvolution

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Adaptive Wavelet Galerkin Methods for Linear Inverse Problems

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Ten Lectures on Wavelets

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Local extremes, runs, strings and multiresolution. (With discussion)

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Nonparametric regression, confidence regions and regularization

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Approximating data with weighted smoothing splines

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On the (bi)infinite case of Shadrin's theorem concerning the \(L_{\infty}\)-boundedness of the \(L_{2}\)-spline projector

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On the global and linear convergence of the generalized alternating direction method of multipliers

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Estimating the Variance In Nonparametric Regression—What is a Reasonable Choice?

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Automated regularization parameter selection in multi-scale total variation models for image restoration

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De-noising by soft-thresholding

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Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition

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Stable recovery of sparse overcomplete representations in the presence of noise

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Ideal spatial adaptation by wavelet shrinkage

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Extensions of smoothing via taut strings

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Multiscale testing of qualitative hypotheses

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Variational principles and Sobolev-type estimates for generalized interpolation on a Riemannian manifold

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Maximum penalized likelihood estimation. Volume II: Regression

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Solution smoothness of ill-posed equations in Hilbert spaces: four concepts and their cross connections

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A New Approach to Source Conditions in Regularization with General Residual Term

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Statistical multiresolution Dantzig estimation in imaging: fundamental concepts and algorithmic framework

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Statistical multiresolution estimation for variational imaging: with an application in Poisson-biophotonics

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Multiscale Change Point Inference

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Scan statistics and applications

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On spatially adaptive estimation of nonparametric regression

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On the \(L_\infty\)-norm of the orthogonal projector onto splines. A short proof of A. Shadrin's theorem

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A distribution-free theory of nonparametric regression

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Asymptotically optimal difference-based estimation of variance in nonparametric regression

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Extreme value analysis of empirical frame coefficients and implications for denoising by soft-thresholding

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Wavelets, approximation, and statistical applications

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Convergence rates for regularization of ill-posed problems in Banach spaces by approximate source conditions

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Nonlinear estimation for linear inverse problems with error in the operator

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Approximate source conditions in Tikhonov–Phillips regularization and consequences for inverse problems with multiplication operators

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A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators

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Convergence rates for Tikhonov regularization based on range inclusions

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Theory of linear ill-posed problems and its applications. Transl., updated and revised from the Russian edition 1978

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Extremes of the standardized Gaussian noise

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Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwidth selectors

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Locally adaptive regression splines

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On Difference-Based Variance Estimation in Nonparametric Regression When the Covariate is High Dimensional

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Approximation in Sobolev spaces by kernel expansions

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Refined error estimates for radial basis function interpolation

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Bandwidth choice for nonparametric regression

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Optimal detection of a jump in the intensity of a Poisson process or in a density with likelihood ratio statistics

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New upper bound for the \(B\)-spline basis condition number II. A proof of de Boor's \(2^k\)-conjecture

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Variational methods in imaging

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The \(L_\infty\)-norm of the \(L_2\)-spline projector is bounded independently of the knot sequence: A proof of de Boor's conjecture

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Exact asymptotics for the scan statistic and fast alternatives

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Tail probabilities for the null distribution of scanning statistics

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Variance estimation for high-dimensional regression models

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An asymptotically optimal window selection rule for kernel density estimates

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Introduction to nonparametric estimation

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Weak convergence and empirical processes. With applications to statistics

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Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy

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Optimal and fast detection of spatial clusters with scan statistics

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Weakly Differentiable Functions

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Identifiers

zbMATH Open document ID

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10.1214/17-AIHP832

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:1650131

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