Multivariate functional principal component analysis for endogenously stratified data

Abstract

We address the problem of performing dimension reduction on multivariate functional data observed on different domains in an endogenously stratified sampling context. The aim is to propose a new multivariate functional principal component analysis \(MFPCA) approach for data sampled by a stratification of a population according to a binary variable of interest. This estimation strategy is derived from a direct relationship between univariate and multivariate FPCA for finite Karhunen-Loève decompositions. The proposed methodology yields encouraging results and can be applied to data with measurement errors. Computational results on simulated data highlight the good performance of the proposed methodology compared to the classical MFPCA, which ignores the type of data sampling. A real-life application considering breast cancer cells data is also presented.