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Estimating the error distribution in nonparametric multiple regression with applications to model testing. (English) Zbl 1185.62078
Summary: We consider the estimation of the error distribution in a heteroscedastic nonparametric regression model with multivariate covariates. As estimator we consider the empirical distribution function of the residuals, which are obtained from multivariate local polynomial fits of the regression and variance functions, respectively. Weak convergence of the empirical residual process to a Gaussian process is proved. We also consider various applications for testing model assumptions in nonparametric multiple regression. The model tests obtained are able to detect local alternatives that converge to zero at an \(n^{-1/2}\)-rate, independent of the covariate dimension. We consider in detail a test for additivity of the regression function.

MSC:
62G08 Nonparametric regression and quantile regression
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62G30 Order statistics; empirical distribution functions
60F05 Central limit and other weak theorems
Software:
R
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