MULTIVARIABLE VARIOGRAM AND ITS APPLICATION TO THE LINEAR-MODEL OF COREGIONALIZATION
MULTIVARIABLE VARIOGRAM AND ITS APPLICATION TO THE LINEAR-MODEL OF COREGIONALIZATION
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DOI：
10.1007/bf02066732
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发表时间：
1991-10-01
期刊：
影响因子：
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通讯作者：
MARCOTTE, D
中科院分区：
文献类型：
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作者：
BOURGAULT, G;MARCOTTE, D
在这篇文章中，我们提出了多变量变差函数，这是定义在一种类似于传统的变差函数，由期望值的距离，平方，在一个空间的p维。 该工具与协区域化的线性模型相结合，提供了一种寻找表征p变量数据集中包含的不同空间尺度的基本变异函数的方法。 在基本成分的数量小于或等于变量的数量的情况下，它是可能的，通过变异函数和交叉变异函数的非线性回归，以直接估计coregionalization参数，以获得基本变量本身，无论是通过协同克里金或直接矩阵求逆。 这个新工具大大简化了Matheron（1982）和Wackernagel（1985）提出的程序。 与Materon方法所需的p（p + 1）/2相反，仅使用一个变差函数（多变量）搜索基本变差函数。 线性协同区域化模型参数的直接估计涉及创建秩为1的半正定协同区域化矩阵。
In this article, we present the multivariable variogram, which is defined in a way similar to that of the traditional variogram, by the expected value of a distance, squared, in a space with p dimensions. Combined with the linear model of coregionalization, this tool provides a way for finding the elementary variograms that characterize the different spatial scales contained in a set of data with p variables. In the case in which the number of elementary components is less than or equal to the number of variables, it is possible, by means of nonlinear regression of variograms and cross-variograms, to estimate the coregionalization parameters directly in order to obtain the elementary variables themselves, either by cokriging or by direct matrix inversion. This new tool greatly simplifies the procedure proposed by Matheron (1982) and Wackernagel (1985). The search for the elementary variograms is carried out using only one variogram (multivariable), as opposed to the p(p + 1)/2 required by the Matheron approach. Direct estimation of the linear coregionalization model parameters involves the creation of semipositive definite coregionalization matrices of rank 1.