Normal approximation in regression

Peter Hall and A. H. Welsh

Journal of Multivariate Analysis, 1991, vol. 39, issue 1, 87-105

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: kernel; estimator; nonparametric; regression; function; estimation; strong; approximation (search for similar items in EconPapers)
Date: 1991
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