Identification and estimation of interaction effects in nonparametric additive regression

Abstract A new formulation of the additive interaction model is introduced. In contrast to existing approaches, the new formulation separates well the joint effects of covariates that cannot be accounted for by individual main effects. The new approach enables correct interpretation of interaction effects by making them orthogonal to the associated main effects in the $ L^{2} $ sense. A new method is developed to estimate the resulting main and interaction effects. Asymptotic $ L^{2} $ error rates are derived for the estimators under mild technical conditions. Numerical evidence is provided via simulation studies and real-data examples.