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Probabilities of maximal deviations for nonparametric regression function estimates

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  • Johnston, Gordon J.

Abstract

Let (X, Y) have regression function m(x) = E(Y X = x), and let X have a marginal density f1(x). We consider two nonparameteric estimates of m(x): the Watson estimate when f1 is known and the Yang estimate when f1 is known or unknown. For both estimates the asymptotic distribution of the maximal deviation from m(x) is proved, thus extending results of Bickel and Rosenblatt for the estimation of density functions.

Suggested Citation

  • Johnston, Gordon J., 1982. "Probabilities of maximal deviations for nonparametric regression function estimates," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 402-414, September.
    • Handle: RePEc:eee:jmvana:v:12:y:1982:i:3:p:402-414
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