Estimating the error distribution in nonparametric multiple regression with applications to model testing

Neumeyer, Natalie;Van Keilegom, Ingrid
(2010) Journal of Multivariate Analysis — Vol. 101, n° 5, p. 1067-1078 (2010)

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Abstract
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(-12)-rate, independent of the covariate dimension. We consider in detail a test for additivity of the regression function. (C) 2010 Elsevier Inc. All rights reserved.
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  • Institution iconUCLouvainSSH/IMAQ - Institut multidisciplinaire pour la modélisation et l'analyse quantitative

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Neumeyer, N., & Van Keilegom, I. (2010). Estimating the error distribution in nonparametric multiple regression with applications to model testing. Journal of Multivariate Analysis, 101(5), 1067-1078. https://doi.org/10.1016/j.jmva.2010.01.007 (Original work published 2010)