Multiple functional regression with both discrete and continuous covariates
This work addresses the need for more flexible regression models in statistics and data analysis, though it appears incremental as it builds on existing kernel-based approaches.
The paper tackles the problem of predicting a functional response using multiple functional covariates, including both discrete and continuous types, by extending functional regression methodology with a nonparametric method based on reproducing kernel Hilbert spaces and positive operator-valued kernels.
In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al. (2010a), the method, which support mixed discrete and continuous explanatory variables, is based on estimating a function-valued function in reproducing kernel Hilbert spaces by virtue of positive operator-valued kernels.