Sharp adaptive estimation of linear functionals.
From MaRDI portal
Publication:1848917
DOI10.1214/aos/1015345955zbMath1043.62029OpenAlexW2025546037MaRDI QIDQ1848917
Alexandre B. Tsybakov, Jussi Klemelä
Publication date: 14 November 2002
Published in: The Annals of Statistics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aos/1015345955
kernel estimationbandwidth selectionminimax riskadaptive curve estimationexact constants in nonparametric smoothing
Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05)
Related Items
Sharp adaptive estimation of quadratic functionals, On adaptive estimation of linear functionals, Nonparametric estimation by convex programming, Exact adaptive pointwise estimation on Sobolev classes of densities, Exact adaptive pointwise drift estimation for multidimensional ergodic diffusions, Estimating linear functionals of a sparse family of Poisson means, Optimal adaptive estimation of a quadratic functional, Unnamed Item, Estimating linear and quadratic forms via indirect observations, Adaptive estimation of linear functionals by model selection, Optimal calibration for multiple testing against local inhomogeneity in higher dimension, Adaptive estimation of the mode of a multivariate density, Pointwise adaptive estimation of a multivariate function, Asymptotically exact minimax estimation in sup-norm for anisotropic Hölder classes, Universal pointwise selection rule in multivariate function estimation, Multidimensional linear functional estimation in sparse Gaussian models and robust estimation of the mean
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Optimal recovery of operators, and related problems
- Learning algorithm for nonparametric filtering
- Optimal rates of convergence for nonparametric estimators
- Asymptotically optimum kernels for density estimation at a point
- Geometrizing rates of convergence. III
- Renormalization exponents and optimal pointwise rates of convergence
- On the solution of an optimal recovery problem and its applications in nonparametric regression
- Risk bounds for model selection via penalization
- Remarks on extremal problems in nonparametric curve estimation
- Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes
- Adaptive estimates of linear functionals
- Asymptotic equivalence of density estimation and Gaussian white noise
- Minimax linear estimation in a white noise problem
- Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwidth selectors
- On spatially adaptive estimation of nonparametric regression
- Optimal pointwise adaptive methods in nonparametric estimation
- Wavelets, approximation, and statistical applications
- Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point
- Progress in data-based bandwidth selection for kernel density estimation
- Sharp adaptation for inverse problems with random noise
- Adaptive minimax estimation of infinitely differentiable functions.
- Adaptive nonparametric estimation of smooth multivariate functions.
- On sharp adaptive estimation of multivariate curves
- Exact constants in inequalities between norms of derivatives of functions
- Kolmogorov-type inequalities and best formulas for numerical differentiation
- On the best approximation of the differentiation operator on the half- line
- Adaptive Spline Estimates for Nonparametric Regression Models
- On a Problem of Adaptive Estimation in Gaussian White Noise
- An Asymptotically Minimax Regression Estimator in the Uniform Norm up to Exact Constant
- Minimax Weights in a Trend Detection Problem of a Random Process
