MULTIVARIATE FUNCTIONAL PRINCIPAL COMPONENT ANALYSIS: A NORMALIZATION APPROACH

We propose an extended version of the classical Karhunen-Loève expansion of a multivariate random process, termed a normalized multivariate functional principal component (mFPCn) representation. This takes variations between the components of the process into account and takes advantage of component dependencies through the pairwise cross-covariance functions. This approach leads to a single set of multivariate functional principal component scores, which serve well as a proxy for multivariate functional data. We derive the consistency properties for the estimates of the mFPCn, and the asymptotic distributions for statistical inferences. We illustrate the finite sample performance of this approach through the analysis of a traffic flow data set, including an application to clustering and a simulation study. The mFPCn approach serves as a basic and useful statistical tool for multivariate functional data analysis.