Goodness-of-fit tests for the error distribution in nonparametric regression
Computational Statistics & Data Analysis
Goodness-of-fit tests in semi-linear models
Statistics and Computing
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In this paper 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 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.