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A0478
Title: Sparse modeling and non-asymptotic bounds via correlation operator of multivariate functional data Authors:  Jun Song - Korea University (Korea, South) [presenting]
Abstract: Functional data analysis has gained significant attention in recent years, particularly in the context of scalar-on-function regression problems involving multivariate functional predictors. However, existing methods for predictor selection in this domain often lack theoretical validity or rely on overly stringent assumptions that may not hold in practice. A novel approach is presented to functional predictor selection that addresses these limitations. Correlation operators are defined for multivariate functional data and identify the core characteristics that form the foundation for theoretical assumptions in sparse methods for multivariate functional data analysis. Building upon this theoretical framework, a novel penalty scheme is introduced for functional regression, which enables deriving superior asymptotic properties under more relaxed and reasonable assumptions. Furthermore, the non-asymptotic behavior of the proposed method is investigated under a finite-sample design, and non-asymptotic bounds are derived to demonstrate selection and estimation consistency. Simulation studies and a real-world application to human brain datasets highlight the effective performance of the method, showcasing its potential to enhance numerous penalized methods for functional data analysis.