Functional PCA With Covariate-Dependent Mean and Covariance Structure

Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of components and predictive performance. However, many existing PCA methods do not make use covariates, those that often have high computational cost or overly simplistic assumptions are violated in practice. In this article, we propose a new framework, called covariate-dependent (CD-FPCA), which both mean covariance structure depend on covariates. We corresponding estimation algorithm, makes spline basis representations roughness penalties, is more computationally efficient than competing approaches adequate prediction accuracy. A key aspect our work novel approach for modeling function ensuring it symmetric positive semidefinite. demonstrate advantages methodology through simulation study an astronomical data analysis.