Exponential bounds of mean error for the kernel estimate of regression functions
type: Item
instance of: scholarly article
title: Exponential bounds of mean error for the kernel estimate of regression functions
zbMATH Open document ID: 0667.62027
DOI: 10.1016/0047-259X(89)90027-4
published in: Journal of Multivariate Analysis
publication date: 1989-01-01T00:00:00Z
review text: Let (X,Y), \((X_ 1,Y_ 1),...,(X_ n,Y_ n)\) be i.d.d. \(R^ r\times R\)-valued random vectors with \(E| Y| <\infty\), and let \(Q_ n(x)\) be a kernel estimate of the regression function \(Q(x)=E(Y|\) \(X=x)\). We establish an exponential bound of the mean deviation between \(Q_ n(x)\) and Q(x) given the training sample \(Z^ n=(X_ 1,Y_ 1,...,X_ n,Y_ n)\), under conditions as weak as possible.
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 4092571
zbMATH Keywords: nonparametric regression
zbMATH Keywords: Besicovitch covering lemma
zbMATH Keywords: kernel estimate
zbMATH Keywords: regression function
zbMATH Keywords: exponential bound
zbMATH Keywords: mean deviation
zbMATH Keywords: training sample
author: Lincheng Zhao
MaRDI profile type: Publication
cites work: On the almost everywhere convergence of nonparametric regression function estimates
cites work: The equivalence of weak, strong, and complete convergence in \(L_ 1\) for kernel density estimates
cites work: Q3336497
cites work: Distribution-free consistency results in nonparametric discrimination and regression function estimation
cites work: On the L 1 convergence of kernel estimators of regression functions with applications in discrimination
cites work: Distribution-free pointwise consistency of kernel regression estimate
cites work: Q5509408
cites work: Consistent window estimation in nonparametric regression
cites work: Q5510038
cites work: Q4135799
cites work: Exponential bounds of mean error for the nearest neighbor estimates of regression functions
cites work: Strong convergence of kernel estimates of nonparametric regression functions
description: scientific article; zbMATH DE number 4092571