A1558
Title: Estimation of causal effects via conditional instrumental variables in functional linear structural equation models
Authors: Michio Yamamoto - The University of Osaka / RIKEN AIP / Shiga University (Japan) [presenting]
Abstract: Functional data analysis provides a flexible framework for modeling data observed over a continuum, such as longitudinal trajectories, temporal signals, and spatial profiles. In many applications, researchers are interested not only in associational relationships among functional variables but also in causal effects. However, causal effect estimation becomes substantially more difficult when unobserved confounding is present. A functional linear structural equation model is considered in which relations among functional variables are represented by linear operators, and identification and estimation of average causal effects using conditional instrumental variables are studied. A central challenge is that the identification equation implied by the model takes the form of an ill-posed inverse problem in an infinite-dimensional space, so standard finite-dimensional instrumental variable arguments do not apply directly. To address this issue, a Tikhonov-regularized estimator for the causal effect is proposed. Theoretical properties of the proposed method are established by deriving a convergence rate for its mean squared error under suitable regularity conditions. Finite-sample performance is also investigated through simulation studies based on synthetic functional data.
