Normal approximation in regression

Peter Hall; A. H. Welsh

doi:10.1016/0047-259X(91)90007-O

Normal approximation in regression

Peter Hall^*, A. H. Welsh

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We obtain a unform 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 convergene 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.

Original language	English
Pages (from-to)	87-105
Number of pages	19
Journal	Journal of Multivariate Analysis
Volume	39
Issue number	1
DOIs	https://doi.org/10.1016/0047-259X(91)90007-O
Publication status	Published - Oct 1991

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10.1016/0047-259X(91)90007-O

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title = "Normal approximation in regression",

abstract = "We obtain a unform 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 convergene 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.",

keywords = "function estimation, kernel estimator, nonparametric regression, strong approximation",

author = "Peter Hall and Welsh, \{A. H.\}",

year = "1991",

month = oct,

doi = "10.1016/0047-259X(91)90007-O",

language = "English",

volume = "39",

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journal = "Journal of Multivariate Analysis",

issn = "0047-259X",

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T1 - Normal approximation in regression

AU - Hall, Peter

AU - Welsh, A. H.

PY - 1991/10

Y1 - 1991/10

N2 - We obtain a unform 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 convergene 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.

AB - We obtain a unform 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 convergene 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.

KW - function estimation

KW - kernel estimator

KW - nonparametric regression

KW - strong approximation

UR - https://www.scopus.com/pages/publications/44949271063

U2 - 10.1016/0047-259X(91)90007-O

DO - 10.1016/0047-259X(91)90007-O

M3 - Article

AN - SCOPUS:44949271063

SN - 0047-259X

VL - 39

SP - 87

EP - 105

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 1

ER -

Normal approximation in regression

Abstract

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