Flexible Spatial Models for Kriging and Cokriging Using Moving Averages and the Fast Fourier Transform (FFT)
Flexible Spatial Models for Kriging and Cokriging Using Moving Averages and the Fast Fourier Transform (FFT)
复制标题
使用移动平均线和快速傅里叶变换 (FFT) 的灵活克里金法和协同克里金法空间模型
DOI：
10.1198/1061860043498
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发表时间：
2004
影响因子：
2.4
通讯作者：
Ronald P. Barry
中科院分区：
文献类型：
--
作者：
J. V. Ver Hoef;N. Cressie;Ronald P. Barry
空间自相关和互相关模型依赖于两个位置之间的距离和方向，并且受到约束，使得对于所有可能的位置集合，模型所隐含的协方差矩阵保持非负定。基于空间相关性，可以构造最优的线性预测器，从不完整和有噪声的空间数据中产生完整的空间场地图。如果数据只有一种变量类型，这种方法称为克里金法，如果数据是两种或两种以上变量类型，则称为协克里金法。在历史上，为了满足非负定条件，Cokriging对交叉变异函数使用了协区域化模型，尽管这类模型不是很灵活。最近的研究表明，移动平均函数可以用来生成一大类有效的、灵活的变差函数模型，并且它们还可以用来生成与分量变差函数兼容的有效交叉变差函数。移动平均方法有几个问题，包括大量的参数和积分困难。本文展示了快速傅立叶变换(FFT)如何解决这些问题。我们考虑的柔性移动平均函数是由许多小矩形组成的，这就消除了积分问题。FFT允许我们计算一组离散滞后上的交叉变异函数；我们展示了如何对任何连续滞后内插交叉变异函数，这允许我们使用标准的最小化例程来拟合灵活的模型。最后给出了仿真算例，验证了该方法的有效性。
Models for spatial autocorrelation and cross-correlation depend on the distance and direction separating two locations, and are constrained so that for all possible sets of locations, the covariance matrices implied from the models remain nonnegative-definite. Based on spatial correlation, optimal linear predictors can be constructed that yield complete maps of spatial fields from incomplete and noisy spatial data. This methodology is called kriging if the data are of only one variable type, and it is called cokriging if it is of two or more variable types. Historically, to satisfy the nonnegative-definite condition, cokriging has used coregionalization models for cross-variograms, even though this class of models is not very flexible. Recent research has shown that moving-average functions may be used to generate a large class of valid, flexible variogram models, and that they can also be used to generate valid cross-variograms that are compatible with component variograms. There are several problems with the moving-average approach, including large numbers of parameters and difficulties with integration. This article shows how the fast Fourier Transform (FFT) solves these problems. The flexible moving-average function that we consider is composed of many small rectangles, which eliminates the integration problem. The FFT allows us to compute the cross-variogram on a set of discrete lags; we show how to interpolate the cross-variogram for any continuous lag, which allows us to fit flexible models using standard minimization routines. Simulation examples are given to demonstrate the methods.