Adaptive estimation of and oracle inequalities for probability densities and characteristic functions
From MaRDI portal
Publication:930649
DOI10.1214/009053607000000965zbMath1360.62118arXiv0806.2909OpenAlexW2054769542MaRDI QIDQ930649
Publication date: 1 July 2008
Published in: The Annals of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0806.2909
minimaxequivalencemean integrated squared errornonparametricinfinite supportblockwise shrinkageinfinitely differentiablenot absolutely integrable
Related Items
Estimating the logarithm of characteristic function and stability parameter for symmetric stable laws, Multivariate density estimation under sup-norm loss: oracle approach, adaptation and independence structure, Adaptive confidence sets in \(L^2\), Honest and adaptive confidence sets in \(L_p\), Pointwise adaptive estimation of a multivariate density under independence hypothesis, Theory of adaptive estimation, Model selection for density estimation with \(\mathbb L_2\)-loss, Adaptive estimation of and oracle inequalities for probability densities and characteristic functions, Sobolev-Hermite versus Sobolev nonparametric density estimation on \(\mathbb{R}\), \(\mathbb{L}_{p}\) adaptive estimation of an anisotropic density under independence hypothesis, Adaptation to lowest density regions with application to support recovery, Minimax bounds for Besov classes in density estimation, Lower bound for estimation of Sobolev densities of order less \(1/2\), A sharp minimax lower bound for the nonparametric estimation of Sobolev densities of order \(1/2\), Adaptive estimation over anisotropic functional classes via oracle approach
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Block thresholding for density estimation: local and global adaptivity
- Oracle inequalities for Efromovich--Pinsker blockwise estimates
- Adaptive density estimation using the blockwise Stein method
- On density estimation in the view of Kolmogorov's ideas in approximation theory
- Nonparametric estimation of a probability density on a Riemannian manifold using Fourier expansions
- Adaptive estimation of and oracle inequalities for probability densities and characteristic functions
- Optimal filtering of square-integrable signals in Gaussian noise
- Nonparametric estimation of smooth probability densities in \(L_ 2\)
- Nonparametric curve estimation. Methods, theory, and applications
- Asymptotic equivalence of density estimation and Gaussian white noise
- Optimal rates and constants in \(L_ 2\)-minimax estimation of probability density functions
- Asymptotically efficient estimation for analytic distributions
- Adaptive wavelet estimation: A block thresholding and oracle inequality approach
- Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
- General empirical Bayes wavelet methods and exactly adaptive minimax estimation
- Asymptotic nonequivalence of nonparametric experiments when the smoothness index is \(1/2\)
- Penalized blockwise Stein's method, monotone oracles and sharp adaptive estimation
- Adaptive minimax estimation of infinitely differentiable functions.
- Nonlinear time series. Nonparametric and parametric methods
- Weighted uniform consistency of kernel density estimators.
- Decoupling inequalities for the tail probabilities of multivariate \(U\)- statistics
- On the second order minimax estimation of distribution functions
- Estimation of the density of regression errors
- A lower-bound oracle inequality for a blockwise-shrinkage estimate
- Empirical Bayes selection of wavelet thresholds
- Adapting to Unknown Smoothness via Wavelet Shrinkage
- Estimation of Distribution Density Belonging to a Class of Entire Functions
- Nonparametric Estimation of a Density of Unknown Smoothness
- Density Estimation Under Random Censorship and Order Restrictions
- A Primer on Statistical Distributions
- Estimation of analytic functions
- Adaptive Estimation of Distribution Density in the Basis of Algebraic Polynomials
- All of Nonparametric Statistics