A0814
Title: Linear structural equation models for functional data with RKHS mapping
Authors: Michio Yamamoto - The University of Osaka / RIKEN AIP / Shiga University (Japan) [presenting]
Yoshikazu Terada - The University of Osaka; RIKEN (Japan)
Abstract: Statistical methods for examining causal relationships in multivariate functional data have significantly developed in recent years. Several approaches are based on structural equation models (SEMs) with function-on-function regression and assume that the functional data lie in a reproducing kernel Hilbert space (RKHS) for theoretical requirements. In practice, however, functional observations may exist in a broader function space. Thus, it is proposed that functional data be mapped into an RKHS before estimation. The theoretical evaluation reveals that pre-mapping to the RKHS can relax the conditions required for ensuring that the regression operators are well-defined in functional linear SEMs. The theoretical findings are further illustrated through numerical examples, highlighting the relaxation of smoothness conditions and the potential for broader applicability in functional data analysis.
