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 L-1 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.

Automated summary

This article proposes a method for studying function-on-function regression models by constructing a tensor product space of reproducing kernel Hilbert spaces and using a model selection approach. It allows for estimating the functional function with functional covariate inputs and detecting interaction effects among the functional covariates.