Adaptive nonparametric confidence sets
From MaRDI portal
Publication:2493553
DOI10.1214/009053605000000877zbMath1091.62039arXivmath/0605473OpenAlexW3104796902MaRDI QIDQ2493553
Aad W. van der Vaart, James M. Robins
Publication date: 21 June 2006
Published in: The Annals of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0605473
Nonparametric regression and quantile regression (62G08) Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Nonparametric tolerance and confidence regions (62G15) Applications of functional analysis in probability theory and statistics (46N30)
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Cites Work
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- A weak invariance principle for weighted \(U\)-statistics with varying kernels
- On the estimation of quadratic functionals
- Spline smoothing in regression models and asymptotic efficiency in \(L_ 2\)
- An asymptotically optimal window selection rule for kernel density estimates
- Adaptive asymptotically minimax estimators of smooth signals
- Learning algorithm for nonparametric filtering
- Optimal filtering of square-integrable signals in Gaussian noise
- Risk bounds for model selection via penalization
- Asymptotically minimax hypothesis testing for nonparametric alternatives. III
- Asymptotic equivalence of density estimation and Gaussian white noise
- Estimation of integral functionals of a density and its derivatives
- Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
- Modulation of estimators and confidence sets.
- Efficient estimation of integral functionals of a density
- Density estimation by wavelet thresholding
- Honest confidence regions for nonparametric regression
- Adaptive estimation of a quadratic functional by model selection.
- Random rates in anisotropic regression. (With discussion)
- Nonparametric goodness-of-fit testing under Gaussian models
- Confidence balls in Gaussian regression.
- Confidence sets for nonparametric wavelet regression
- Adaptive confidence balls
- [https://portal.mardi4nfdi.de/wiki/Publication:3048064 Estimation des densit�s: risque minimax]
- Adapting to Unknown Smoothness via Wavelet Shrinkage
- Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates
- Minimum complexity density estimation
- Asymptotic Statistics
- Ideal spatial adaptation by wavelet shrinkage
- REACT Scatterplot Smoothers: Superefficiency through Basis Economy
- On a Problem of Adaptive Estimation in Gaussian White Noise
- Introduction to nonparametric estimation
- Gaussian model selection