Adaptive estimation of linear functionals in functional linear models
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Publication:1933354
DOI10.3103/S1066530712030027zbMath1283.62142arXiv1112.2855OpenAlexW2066153074MaRDI QIDQ1933354
Publication date: 23 January 2013
Published in: Mathematical Methods of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1112.2855
Sobolev spacemodel selectionlinear functionaladaptationLepski's methodpointwise estimationlinear Galerkin projectionlocal average estimationminimax-theory
Asymptotic properties of nonparametric inference (62G20) Linear regression; mixed models (62J05) Nonparametric estimation (62G05)
Cites Work
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- Bandwidth selection in kernel density estimation: oracle inequalities and adaptive minimax optimality
- Adaptive functional linear regression
- CLT in functional linear regression models
- High-dimensional Gaussian model selection on a Gaussian design
- Methodology and convergence rates for functional linear regression
- Smoothing splines estimators for functional linear regression
- Thresholding projection estimators in functional linear models
- Minimaxity of the method of regularization on stochastic processes
- Renormalization exponents and optimal pointwise rates of convergence
- Risk bounds for model selection via penalization
- Statistical estimation and optimal recovery
- A constrained risk inequality with applications to nonparametric functional estimation
- Flexible smoothing with \(B\)-splines and penalties. With comments and a rejoinder by the authors
- Adaptive prediction and estimation in linear regression with infinitely many parameters.
- Optimal prediction for linear regression with infinitely many parameters.
- On rate optimal local estimation in functional linear regression
- Adaptive estimation of linear functionals by model selection
- Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes
- Generalized functional linear models
- Nonlinear estimation for linear inverse problems with error in the operator
- Beiträge zur Störungstheorie der Spektralzerlegung
- Interpolation in variable Hilbert scales with application to inverse problems
- On Nonparametric Estimation of the Value of a Linear Functional in Gaussian White Noise
- When Do Sobolev Spaces Form a Hilbert Scale?
- An a Posteriori Parameter Choice for Tikhonov Regularization in Hilbert Scales Leading to Optimal Convergence Rates
- Tikhonov Regularization for Finitely and Infinitely Smoothing Operators
- On inverse problems with unknown operators
- On a Problem of Adaptive Estimation in Gaussian White Noise
- Error bounds for tikhonov regularization in hilbert scales
