Functional Principal Components Analysis of Spatially Correlated Data

• DOI: 10.48550/arxiv.1411.4681
• Publication Date: 2014-01-01
• Authors: Chong Liu; Surajit Ray; Giles Hooker
• Keywords: Spatial correlation; Spatial Dependence

This paper focuses on the analysis of spatially correlated functional data. The between-curve correlation is modeled by correlating principal component scores We propose a Spatial Principal Analysis Conditional Expectation framework to explicitly estimate spatial correlations and reconstruct individual curves. approach works even when observed data per curve are sparse. Assuming stationarity, empirical calculated as ratio eigenvalues smoothed covariance surface $Cov(X_i(s),X_i(t))$ cross-covariance $Cov(X_i(s), X_j(t))$ at locations indexed $i$ $j$. Then anisotropy Matérn model fit correlations. Finally, estimated sparsely can naturally accommodate arbitrary structures, but there an enormous reduction in computation if one assume separability temporal components. hypothesis tests examine well isotropy effect correlation. Simulation studies applications show improvements reconstruction using our over method where curves assumed be independent. In addition, we that asymptotic properties estimates uncorrelated case still hold 'mild' assumed.