A nonparametric concurrent regression model with multivariate functional inputs

Regression models with functional responses and covariates have attracted extensive research. Nevertheless, there is no existing method for the situation where the functional covariates are bivariate functions with one of the variables in common with the response function. In this article, we propose a nonparametric function-on-function regression method. We construct model spaces using a Gaussian kernel function and smoothing spline ANOVA decomposition. We estimate the nonparametric function using penalized likelihood and study properties of the Gaussian kernel function and the convergence rate of the proposed estimation method. We evaluate the proposed methods using simulations and illustrate them using two real data examples.