Functional principal component analysis of spatially correlated data

This paper focuses on the analysis of spatially correlated functional data. We propose a parametric model for spatial correlation and the between-curve correlation is modeled by correlating functional principal component scores of the functional data. Additionally, in the sparse observation framework, we propose a novel approach of spatial principal analysis by conditional expectation to explicitly estimate spatial correlations and reconstruct individual curves. Assuming spatial stationarity, empirical spatial correlations are calculated as the ratio of eigenvalues of the smoothed covariance surface Cov(Xi (s), Xi (t)) and crosscovariance surface Cov(Xi (s), X j (t)) at locations indexed by i and j . Then a anisotropy Matérn spatial correlation model is fitted to empirical correlations. Finally, principal component scores are estimated to reconstruct the sparsely observed curves. This framework can naturally accommodate arbitrary covariance structures, but there is an enormous reduction in computation if one can assume the separability of temporal and spatial components. We demonstrate the consistency of our estimates and propose hypothesis tests to examine the separability as well as the isotropy effect of spatial correlation. Using simulation studies, we show that these Electronic supplementary material The online version of this article (doi:10.1007/s11222-016-9708-4) contains supplementary material, which is available to authorized users. B Surajit Ray [email protected] 1 State Street Global Advisors, Boston, USA 2 School of Mathematics and Statistics, University of Glasgow, Glasgow, UK 3 Department of Statistical Science and Department of Biological Statistics and Computational Biology, Cornell University, New York, USA methods have some clear advantages over existing methods of curve reconstruction and estimation of model parameters.