A1079
Title: Functional structural equation models
Authors: Kuang-Yao Lee - Temple University (United States) [presenting]
Lexin Li - University of California Berkeley (United States)
Abstract: A functional structural equation model is introduced for estimating directional relations from multivariate functional data. The estimation is decoupled into two major steps: directional order determination and selection through sparse functional regression. A score function is first proposed at the linear operator level. It shows that its minimization can recover the true directional order when the relation between each function and its parental functions is nonlinear. A sparse functional additive regression is then developed, where both the response and the multivariate predictors are functions, and the regression relation is additive and nonlinear. Strategies are also proposed to speed up the computation and scale the method. In theory, the consistencies of order determination are established, sparse functional additive regression, and directed acyclic graph estimation while allowing both the dimension of the Karhunen-Loeve expansion coefficients and the number of random functions to diverge with the sample size. The efficacy of the method is illustrated through simulations and an application to brain-effective connectivity analysis.
