Abstract
A simple consistent test of additivity in a multiple nonparametric regression model is proposed, where data are observed on a lattice. The new test is based on an estimator of the L 2-distance between the (unknown) nonparametric regression function and its best approximation by an additive nonparametric regression model. The corresponding test-statistic is the difference of a classical ANOVA style statistic in a two-way layout with one observation per cell and a variance estimator in a homoscedastic nonparametric regression model. Under the null hypothesis of additivity asymptotic normality is established with a limiting variance which involves only the variance of the error of measurements. The results are extended to models with an approximate lattice structure, a heteroscedastic error structure and the finite sample behaviour of the proposed procedure is investigated by means of a simulation study.
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Derbort, S., Dette, H. & Munk, A. A Test for Additivity in Nonparametric Regression. Annals of the Institute of Statistical Mathematics 54, 60–82 (2002). https://doi.org/10.1023/A:1016113704805
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DOI: https://doi.org/10.1023/A:1016113704805