Functional Principal Component Analysis for Extrapolating Multistream Longitudinal Data

Abstract

In this article, we present a nonparametric approach to predict the evolution of multistream longitudinal data. Our approach first decomposes each stream into a linear combination of eigenfunctions and their corresponding functional principal component (FPC) scores. A Gaussian process prior for the FPC scores is then induced based on a functional semimetric that introduces a similarity measure across streams. Finally, an empirical Bayesian updating strategy is derived to update the established prior using real-time stream data. Empirical evidence shows that the proposed framework outperforms state-of-the-art approaches and can effectively account for heterogeneity as well as achieve high predictive accuracy.