Upper functions for positive random functionals. I: General setting and Gaussian random functions

DOI10.3103/S1066530713010018zbMath1279.60033MaRDI QIDQ359388

O. V. Lepskij

Publication date: 12 August 2013

Published in: Mathematical Methods of Statistics (Search for Journal in Brave)

zbMATH Keywords

empirical processesdoubling measuremetric entropyupper functionGaussian random function

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Density estimation (62G07) Gaussian processes (60G15) Inequalities; stochastic orderings (60E15)

Related Items

Upper functions for \(\mathbb{L}_{p}\)-norms of Gaussian random fields, Multivariate density estimation under sup-norm loss: oracle approach, adaptation and independence structure, Upper functions for positive random functionals. II. Application to the empirical processes theory. I, Upper functions for positive random functionals. II: Application to the empirical processes theory, Part 2, A sup-norm oracle inequality for a partially linear regression model, A new approach to estimator selection, Adaptive estimation under single-index constraint in a regression model, Adaptive invariant density estimation for ergodic diffusions over anisotropic classes, Structural adaptive deconvolution under \({\mathbb{L}_p}\)-losses, Concentration of scalar ergodic diffusions and some statistical implications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Risk hull method and regularization by projections of ill-posed inverse problems
• Uniform bounds for norms of sums of independent random functions
• Probability inequalities for empirical processes and a law of the iterated logarithm
• Some limit theorems for empirical processes (with discussion)
• Structural adaptation via \(\mathbb L_p\)-norm oracle inequalities
• Universal pointwise selection rule in multivariate function estimation
• Additive regression and other nonparametric models
• Upper functions and oscillating Gaussian processes
• Risk bounds for model selection via penalization
• Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes
• Sharper bounds for Gaussian and empirical processes
• Adaptive hypothesis testing using wavelets
• Optimal pointwise adaptive methods in nonparametric estimation
• A Bennett concentration inequality and its application to suprema of empirical processes
• Rates of strong uniform consistency for multivariate kernel density estimators. (Vitesse de convergence uniforme presque sûre pour des estimateurs à noyaux de densités multivariées)
• About the constants in Talagrand's concentration inequalities for empirical processes.
• Weak convergence and empirical processes. With applications to statistics
• Exponential bounds for minimum contrast estimators
• Concentration inequalities and asymptotic results for ratio type empirical processes
• Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates
• Local and Global Upper Functions for Random Fields
• The Generic Chaining
• Asymptotic Properties of Gaussian Processes