Normal approximation in regression
type: Item
instance of: scholarly article
title: Normal approximation in regression
zbMATH Open document ID: 0748.62010
DOI: 10.1016/0047-259X(91)90007-O
author: Alan H. Welsh
author: Peter Hall
published in: Journal of Multivariate Analysis
publication date: 1992-06-28T00:00:00Z
review text: We obtain a uniform strong approximation for the distribution of a Nadaraya-Watson kernel estimator of a regression function. The approximation is obtained for general multivariate explanatory variables under an algebraic moment condition on the errors. A stronger rate of convergence result for the normal approximation is obtained at the expense of stronger moment conditions. We use the strong approximation results to derive a normal approximation to the distribution of the fitted values from the model.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 31990
zbMATH Keywords: nonparametric regression
zbMATH Keywords: function estimation
zbMATH Keywords: uniform strong approximation
zbMATH Keywords: Nadaraya-Watson kernel estimator
zbMATH Keywords: general multivariate explanatory variables
zbMATH Keywords: algebraic moment condition on the errors
zbMATH Keywords: rate of convergence
zbMATH Keywords: normal approximation
reviewed by: A. D. Barbour
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 31990