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Functional principal component analysis of spatially correlated data

机译：空间相关数据的功能主成分分析

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摘要

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)) 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 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.
机译：本文着重分析与空间相关的功能数据。我们提出了一种用于空间相关性的参数模型，并且通过关联功能数据的功能主成分评分来建模曲线间相关性。此外，在稀疏观测框架中，我们提出了一种通过条件期望进行空间主体分析的新颖方法，以明确估计空间相关性并重建单个曲线。假设空间平稳性，将经验空间相关性计算为位置处的平滑协方差曲面Cov（Xi（s），Xi（t））和交叉协方差曲面Cov（Xi（s），Xj（t））的特征值之比由i和j索引。然后将各向异性Matern空间相关模型拟合到经验相关。最后，估计主成分分数以重建稀疏观察到的曲线。这种框架自然可以容纳任意协方差结构，但是如果可以假设时间和空间分量的可分离性，则可以大大减少计算量。我们证明了我们的估计的一致性，并提出了假设检验来检验空间相关性的可分离性和各向同性效应。通过仿真研究，我们表明这些方法比现有的曲线重构和模型参数估计方法具有明显优势。

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