Flexible Modeling of Variable Asymmetries in Cross-Covariance Functions for Multivariate Random Fields
Flexible Modeling of Variable Asymmetries in Cross-Covariance Functions for Multivariate Random Fields
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DOI：
10.1007/s13253-020-00414-2
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发表时间：
2020-09
期刊：
影响因子：
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通讯作者：
G. A. Qadir;C. Euán;Ying Sun
中科院分区：
文献类型：
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作者：
G. A. Qadir;C. Euán;Ying Sun
多变量空间数据的地质统计分析用于推理和联合预测（共同克里格）通常依赖于边际和交叉协方差函数的建模。前者量化变量内部的空间依赖性，后者量化不同变量之间的空间依赖性。边际协方差函数总是对称的；然而，交叉协方差函数在实际数据中往往表现出不对称性。非对称交叉协方差意味着在变量的固定顺序上交换位置的交叉协方差值的变化。这种交叉协方差值的变化往往是由于一个变量对另一个变量的响应所产生的空间延迟造成的。这些空间延迟在环境过程中很常见，特别是在涉及盛行风和洋流等动态现象时。在这里，我们提出了一种新的方法来引入灵活的不对称的交叉协方差的平稳多元协方差函数。提出的方法包括建模约束交叉光谱特征的相位分量，以允许不对称交叉协方差。通过多次模拟研究，我们证明了我们提出的模型能够恢复交叉依赖结构，并改进传统模型的空间预测。此外，我们在颗粒物浓度（）、风速和相对湿度的真实三元数据集上说明了我们的方法。实际数据示例表明，我们的方法在模型拟合和空间预测方面优于传统使用的模型。本文附带的补充材料出现在网上。
The geostatistical analysis of multivariate spatial data for inference as well as joint predictions (co-kriging) ordinarily relies on modeling of the marginal and cross-covariance functions. While the former quantifies the spatial dependence within variables, the latter quantifies the spatial dependence across distinct variables. The marginal covariance functions are always symmetric; however, the cross-covariance functions often exhibit asymmetries in the real data. Asymmetric cross-covariance implies change in the value of cross-covariance for interchanged locations on fixed order of variables. Such change of cross-covariance values is often caused due to the spatial delay in effect of the response of one variable on another variable. These spatial delays are common in environmental processes, especially when dynamic phenomena such as prevailing wind and ocean currents are involved. Here, we propose a novel approach to introduce flexible asymmetries in the cross-covariances of stationary multivariate covariance functions. The proposed approach involves modeling the phase component of the constrained cross-spectral features to allow for asymmetric cross-covariances. We show the capability of our proposed model to recover the cross-dependence structure and improve spatial predictions against traditionally used models through multiple simulation studies. Additionally, we illustrate our approach on a real trivariate dataset of particulate matter concentration (), wind speed and relative humidity. The real data example shows that our approach outperforms the traditionally used models, in terms of model fit and spatial predictions.Supplementary materials accompanying this paper appear on-line.