Multivariate functional generalized additive models

This paper studies a regression with multiple functional predictors and a scalar response. The proposed model, which we called multivariate functional generalized additive model (mFGAM), extends the usual linear regression model in two key respects. First, mFGAM uses group minimax concave penalty (gMCP) to efficiently deal with high-dimensional problems involving a large number of functional predictors. Second, mFGAM extends beyond the standard linear regression setting to fit general non-linear additive models, and mFGAM is more flexible than multivariate functional generalized linear model (mFGLM). This model is different from McLean et al. [Functional generalized additive models. J Comput Graph Stat. 2014;23(1):249-269.] since their model cannot deal with the situation where the number of parameters is bigger than the sample size. The simulation studies and the application are performed to demonstrate the accuracy and stability of the proposed model.