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Estimating the error distribution function in nonparametric regression with multivariate covariates. (English) Zbl 1158.62032
Summary: We consider nonparametric regression models with multivariate covariates and estimate the regression curve by an undersmoothed local polynomial smoother. The resulting residual-based empirical distribution function is shown to differ from the error-based empirical distribution function by the density times the average of the errors, up to a uniformly negligible remainder term. This result implies a functional central limit theorem for the residual-based empirical distribution function.

MSC:
62G08 Nonparametric regression and quantile regression
62G30 Order statistics; empirical distribution functions
60F17 Functional limit theorems; invariance principles
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