🤖 AI Summary
This study addresses the challenge of extracting principal components from sparse and irregularly observed multivariate functional data, particularly in longitudinal settings where modeling cross-variable dependencies is difficult. To overcome the limitations of conventional approaches that rely on univariate scores and subsequent eigendecomposition, the authors propose a novel framework that directly estimates multivariate functional principal components by integrating maximum likelihood estimation with a modified Gram–Schmidt orthogonality constraint. This approach more accurately captures the covariance structure among variables. Empirical evaluations on datasets comprising Alzheimer’s disease cognitive biomarkers and Irish dairy cow milk production demonstrate that the proposed method yields substantially improved estimation accuracy and interpretability of principal components compared to existing techniques.
📝 Abstract
Traditional Functional Principal Component Analysis typically focuses on densely observed univariate functional data, yet many applications, particularly in longitudinal studies, involve multivariate functional data observed sparsely and irregularly across subjects. A common approach for extracting multivariate functional principal components in such settings relies on an eigen decomposition of univariate functional principal component scores to capture cross-component correlations. We propose a new approach for the estimation of multivariate functional principal components by improving the univariate eigenanalysis through maximum likelihood estimation combined with a modified Gram-Schmidt orthonormalization. The performance of the proposed approach is evaluated against two established methods, and its practical utility is demonstrated through an application to longitudinal cognitive biomarker data from an Alzheimer's disease study and a collection of data on dairy milk yield and milk compositions from research dairy farms in Ireland.