Functional principal component analysis of spatially correlated data

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 $$(X_i(s),X_i(t))$$ ( X i ( s ) , X i ( t ) ) and cross-covariance surface Cov $$(X_i(s), X_j(t))$$ ( X i ( 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 methods have some clear advantages over existing methods of curve reconstruction and estimation of model parameters. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistics and Computing Springer Journals

Functional principal component analysis of spatially correlated data

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Publisher
Springer US
Copyright
Copyright © 2016 by The Author(s)
Subject
Statistics; Statistics and Computing/Statistics Programs; Artificial Intelligence (incl. Robotics); Statistical Theory and Methods; Probability and Statistics in Computer Science
ISSN
0960-3174
eISSN
1573-1375
D.O.I.
10.1007/s11222-016-9708-4
Publisher site
See Article on Publisher Site

Abstract

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 $$(X_i(s),X_i(t))$$ ( X i ( s ) , X i ( t ) ) and cross-covariance surface Cov $$(X_i(s), X_j(t))$$ ( X i ( 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 methods have some clear advantages over existing methods of curve reconstruction and estimation of model parameters.

Journal

Statistics and ComputingSpringer Journals

Published: Oct 4, 2016

References

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