Normal approximation in regression

Peter Hall*, A. H. Welsh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)87-105
Number of pages19
JournalJournal of Multivariate Analysis
Issue number1
Publication statusPublished - Oct 1991


Dive into the research topics of 'Normal approximation in regression'. Together they form a unique fingerprint.

Cite this