Estimating the error distribution function in nonparametric regression with multivariate covariates

Ursula U. Müller, Anton Schick and Wolfgang Wefelmeyer

Statistics & Probability Letters, 2009, vol. 79, issue 7, 957-964

Abstract: 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.

Date: 2009
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