Testing for additivity in non‐parametric regression

Abstract

AbstractThis article discusses a novel approach for testing for additivity in non‐parametric regression. We represent the model using a linear mixed model 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 test 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 alternatives and apply the methods to a diabetes data set. The Canadian Journal of Statistics 44: 445–462; 2016 © 2016 Statistical Society of Canada