Testing for additivity in nonparametric regression

This paper discusses a novel approach for testing for additivity in nonparametric regression. We represent the model using a linear mixedmodel framework and equivalently rewrite the original testing problem as testing for a subset of zero variance components. We propose two testing procedures: the restricted likelihood ratio test and the generalized F test. We develop the finite sample null distribution of the restricted likelihood ratio testing and generalized F test using the spectral decomposition of the restricted likelihood ratio and the residual sum of squares respectively. The null distribution is non-standard and we provide a fast algorithm to simulate from the null distribution of the tests. We show, through numerical investigation, that the proposed testing procedures outperform the available methods. And we apply the proposed method to a diabetes dataset. The Canadian Journal of Statistics xx: 1–25; 20?? c © 20?? Statistical Society of Canada Résumé: Insérer votre résumé ici. We will supply a French abstract for those authors who can’t prepare it themselves. La revue canadienne de statistique xx: 1–25; 20?? c © 20?? Société statistique du Canada c © 20?? Statistical Society of Canada / Société statistique du Canada CJS ??? 2 Vol. xx, No. yy