Bracketing smooth functions
type: Item
instance of: scholarly article
title: Bracketing smooth functions
zbMATH Open document ID: 0811.60025
DOI: 10.1016/0304-4149(94)90102-3
published in: Stochastic Processes and their Applications
publication date: 1995-05-02T00:00:00Z
review text: Let \({\mathcal F}\) be the class of functions \(f: R^ d\to R\) which are \(\alpha\)-times differentiable with derivatives bounded by numbers \(M_ j\) on each given set \(I_ j\) in a partition of \(R^ d= \bigcup_ j I_ j\). Upper and lower bounds on the \(L_ 2(P)\)-bracketing entropy of \({\mathcal F}\) are obtained. Some consequences of the bounds for empirical laws of large numbers and central limit theorems are given.
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 672062
zbMATH Keywords: bracketing number
zbMATH Keywords: entropy
zbMATH Keywords: empirical laws of large numbers
zbMATH Keywords: central limit theorems
author: Aad van der Vaart
reviewed by: K. Kubilius
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)90102-3
OpenAlex ID: W2072124224
cites work: Q3217346
cites work: Q5512461
cites work: Q3742418
cites work: Metric entropy and approximation
cites work: A central limit theorem under metric entropy with \(L_ 2\) bracketing
description: scientific article; zbMATH DE number 672062