Functional principal component analysis of spatially correlated data

Article English OPEN
Liu, Chong ; Ray, Surajit ; Hooker, Giles (2017)
  • Publisher: Springer
  • Journal: Statistics and Computing
  • Related identifiers: doi: 10.1007/s11222-016-9708-4, doi: 10.13039/100000001
  • Subject: Theoretical Computer Science | Computational Theory and Mathematics | Statistics, Probability and Uncertainty | Statistics and Probability | HA

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))(Xi(s),Xi(t)) and cross-covariance surface Cov (Xi(s),Xj(t))(Xi(s),Xj(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.
  • References (31)
    31 references, page 1 of 4

    Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions. Dover, New York (1970)

    Abramowitz, M., Stegun, I.A., et al.: Handbook of mathematical functions. Appl. Math. Ser. 55, 62 (1966)

    Aston, J.A., Pigoli, D., Tavakoli, S.: Tests for separability in nonparametric covariance operators of random surfaces. arXiv preprint arXiv:1505.02023 (2015)

    Avriel, M.: Nonlinear Programming: analysis and Methods. Courier Corporation, New York (2003)

    Baladandayuthapani, V., Mallick, B.K.: Young Hong, M., Lupton, J.R., Turner, N.D., Carroll, R.J.: Bayesian hierarchical spatially correlated functional data analysis with application to colon carcinogenesis. Biometrics 64(1), 64-73 (2008)

    Banerjee, S., Johnson, G.A.: Coregionalized single-and multiresolution spatially varying growth curve modeling with application to weed growth. Biometrics 62(3), 864-876 (2006)

    Bowman, A. W. and Azzalini, A.: R package sm: nonparametric smoothing methods (version 2.2-5), University of Glasgow, UK and Universita` di Padova, Italia. adrian/sm, (2013)

    Cressie, N.: Statistics for Spatial Data. Wiley, New York (2015)

    Diggle, P.J., Ribeiro Jr., P.J., Christensen, O.F.: An Introduction to Model-Based Geostatistics, Spatial Statistics and Computational Methods, pp. 43-86. Springer, New York (2003)

    Gromenko, O., Kokoszka, P., Zhu, L., Sojka, J.: Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends. Ann. Appl. Stat. 6(2), 669-696 (2012). doi:10.1214/11-AOAS524

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