Detection of Interaction Effects in a Nonparametric Concurrent Regression Model

Many methods have been developed to study nonparametric function-on-function regression models. Nevertheless, there is a lack of model selection approach to the regression function as a functional function with functional covariate inputs. To study interaction effects among these functional covariates, in this article, we first construct a tensor product space of reproducing kernel Hilbert spaces and build an analysis of variance (ANOVA) decomposition of the tensor product space. We then use a model selection method with the [Formula: see text] criterion to estimate the functional function with functional covariate inputs and detect interaction effects among the functional covariates. The proposed method is evaluated using simulations and stroke rehabilitation data.