Estimation of Multivariate Functional Principal Components from Sparse Functional Data

TL;DR

This paper introduces a new maximum likelihood-based method for estimating multivariate functional principal components from sparsely observed data, improving upon existing techniques and demonstrating practical utility in biomedical and agricultural studies.

Contribution

A novel estimation approach combining maximum likelihood and modified Gram-Schmidt orthonormalization for multivariate functional PCA from sparse data.

Findings

Outperforms existing methods in simulation studies.

Effectively captures cross-component correlations.

Successfully applied to Alzheimer's biomarker and dairy farm data.

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.