Coherence for Multivariate Random Fields
Coherence for Multivariate Random Fields
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DOI：
10.5705/ss.202015.0309
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发表时间：
2018
影响因子：
1.4
通讯作者：
W. Kleiber
中科院分区：
文献类型：
--
作者：
W. Kleiber
多变量空间场数据越来越常见，其建模通常依赖于构建互协方差函数来描述跨进程关系。另一种观点是对谱测度矩阵进行建模。我们开发的概念的一致性，相位和增益的多维平稳过程。相干性作为频率的函数，是在该频率下两个空间过程之间的线性关系的量度。我们使用相干函数来说明一些以前提出的多变量过程的构造的基本限制，这表明这些选项是不可行的数据建模。我们还给出了自然的解释Matérn类的互协方差参数，其中的交叉平滑控制在无限高的频率的相干性的衰减，和跨范围参数控制的频率最大的相干性。这些解释为暗示变量之间可能存在非物理关系的特定参数组合提供了警告。从平滑的多变量周期图矩阵估计。我们说明了两个数据集，预测和再分析海平面气压和赤道地区的位势高度的估计和解释这些功能。中国统计：预印本doi：10.5705/ss.202015.0309
Multivariate spatial field data are increasingly common and their modeling typically relies on building cross-covariance functions to describe crossprocess relationships. An alternative viewpoint is to model the matrix of spectral measures. We develop the notions of coherence, phase, and gain for multidimensional stationary processes. Coherence, as a function of frequency, is a measure of linear relationship between two spatial processes at that frequency. We use the coherence function to illustrate fundamental limitations on a number of previously proposed constructions for multivariate processes, suggesting these options are not viable for data modeling. We also give natural interpretations to cross-covariance parameters of the Matérn class, where the cross-smoothness controls the decay of coherence at infinitely high frequencies, and the cross-range parameter controls the frequency of greatest coherence. These interpretations provide warnings for particular parameter combinations that imply potentially non-physical relationships between variables. Estimation follows from smoothed multivariate periodogram matrices. We illustrate the estimation and interpretation of these functions on two datasets, forecast and reanalysis sea level pressure and geopotential heights over the equatorial region. Statistica Sinica: Preprint doi:10.5705/ss.202015.0309