Multivariate functional group sparse regression: functional predictor selection
This work addresses functional predictor selection for high-dimensional data, with applications in neuroimaging to identify brain regions linked to ADHD and IQ, representing an incremental advancement in functional regression methods.
The authors tackled the problem of selecting relevant functional predictors and estimating smooth functional coefficients in high-dimensional multivariate functional data, achieving consistent selection and estimation with demonstrated effectiveness in simulations and fMRI applications.
In this paper, we propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under high-dimensional multivariate functional data setting. In particular, we develop two methods for functional group-sparse regression under a generic Hilbert space of infinite dimension. We show the convergence of algorithms and the consistency of the estimation and the selection (oracle property) under infinite-dimensional Hilbert spaces. Simulation studies show the effectiveness of the methods in both the selection and the estimation of functional coefficients. The applications to the functional magnetic resonance imaging (fMRI) reveal the regions of the human brain related to ADHD and IQ.