How to get central limit theorems for global errors of estimates.
type: Item
instance of: scholarly article
title: How to get central limit theorems for global errors of estimates.
zbMATH Open document ID: 1060.62056
DOI: 10.1023/A:1022240820668
published in: Applications of Mathematics
publication date: 2005-05-04T00:00:00Z
full work available at URL: https://eudml.org/doc/33028
review text: The paper pays attention to global statistical errors in a nonparametric model with i.i.d.\ observations, such as the \(L_p\)-norm of differences, or information divergences, between estimates. The paper reviews the techniques leading to normal asymptotic laws for global errors, such as strong approximation and martingale theory of Poissonization. The preferences between these techniques usually depend on what estimator is taken into account. The author considers mainly the kernel and so-called Barron estimators. The latter are convex mixtures of the histogram and a priori given densities with the weights of the histogram tending to 1 as the sample size tends to infinity.
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60F25
zbMATH DE Number: 2165518
zbMATH Keywords: limit theorems
zbMATH Keywords: Poissonization
zbMATH Keywords: global errors
zbMATH Keywords: strong approximation
zbMATH Keywords: empirical processes
zbMATH Keywords: U-statistics
author: Alain Berlinet
MaRDI profile type: Publication
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OpenAlex ID: W163261952
description: scientific article; zbMATH DE number 2165518