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B0388
Title: Models for sparse and spatially correlated functional data Authors:  Surajit Ray - University of Glasgow (United Kingdom) [presenting]
Giles Hooker - Cornell University (United States)
Chong Liu - State Street Global Advisors (United States)
Abstract: The analysis of geo-spatially correlated functional data is considered. The between-curve correlation is modeled by correlating functional principal component scores of the functional data. We propose a Spatial Principal Analysis by Conditional Expectation framework to explicitly estimate spatial correlations and reconstruct individual curves. This approach works even when the observed data per curve are sparse. Assuming spatial stationarity, empirical spatial correlations are calculated as the ratio of eigenvalues of the smoothed covariance surface $Cov(X_i(s),X_i(t))$ and cross-covariance surface $Cov(X_i(s),X_j(t))$ at locations indexed by $i$ and $j$. Then a anisotropy Matern spatial correlation model is fit 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 propose hypothesis tests to examine the separability as well as the isotropy effect of spatial correlation. Simulation studies and applications of empirical data show improvements in the curve reconstruction using our framework over the method where curves are assumed to be independent.