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Normal approximation in regression

Author

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  • Hall, Peter
  • Welsh, A. H.

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.

Suggested Citation

  • Hall, Peter & Welsh, A. H., 1991. "Normal approximation in regression," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 87-105, October.
    • Handle: RePEc:eee:jmvana:v:39:y:1991:i:1:p:87-105
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