NONPARAMETRIC-ESTIMATION OF NONSTATIONARY SPATIAL COVARIANCE STRUCTURE
NONPARAMETRIC-ESTIMATION OF NONSTATIONARY SPATIAL COVARIANCE STRUCTURE
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DOI：
10.2307/2290458
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发表时间：
1992-03-01
影响因子：
3.7
通讯作者：
GUTTORP, P
中科院分区：
文献类型：
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作者：
SAMPSON, PD;GUTTORP, P
空间过程协方差结构的估计是空间插值问题和监测网设计的基本前提。本文介绍了一种非参数方法来全局估计随机函数Z（x，t）在时间t（i）（i = 1，. T）在有限数量的采样站x（i）（i = 1，2，.，N）在飞机上。我们的分析假设时间平稳性，但不假设空间平稳性（或各向同性）。我们分析空间分散var（Z（x（i），t）- Z（x（j），t））作为空间协方差结构的自然度量，并将其建模为站点对（x（i），x（j））的地理坐标的一般平滑函数。该模型分两步构建。首先，使用非度量多维标度（MDS），我们计算一个二维表示的采样站的点间距离的单调函数-三角洲（ij）近似的空间分散。MDS转换成一个问题的协方差结构，表示在空间分散，是固定的和各向同性的。其次，我们计算薄板样条，以提供平滑的映射到他们的MDS表示的采样站的地理表示。该映射f和从MDS导出的单调函数g的组合产生var（Z（x（a），t）- Z（x（B），t））对于任意两个地理位置x（a）和x（B）（监测或不监测）的形式g（\f（x（a））- f（x（B））\）的非参数估计。通过限制单调函数g的一类条件非正定变差函数，我们确保所得到的非参数模型对应于一个非负定协方差模型。我们使用双正交网格，介绍了Bookstein在形态学领域，描绘薄板样条映射，体现了样本协方差矩阵的各向异性和非平稳性的性质。对不列颠哥伦比亚省西南部监测到的太阳辐射中尺度变化的分析证明了这种方法。
Estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks. We introduce a nonparametric approach to global estimation of the spatial covariance structure of a random function Z(x, t) observed repeatedly at times t(i) (i = 1, ..., T) at a finite number of sampling stations x(i) (i = 1, 2, ..., N) in the plane. Our analyses assume temporal stationarity but do not assume spatial stationarity (or isotropy). We analyze the spatial dispersions var(Z(x(i), t) - Z(x(j), t)) as a natural metric for the spatial covariance structure and model these as a general smooth function of the geographic coordinates of station pairs (x(i), x(j)). The model is constructed in two steps. First, using nonmetric multidimensional scaling (MDS) we compute a two-dimensional representation of the sampling stations for which a monotone function of interpoint distances-delta(ij) approximates the spatial dispersions. MDS transforms the problem into one for which the covariance structure, expressed in terms of spatial dispersions, is stationary and isotropic. Second, we compute thin-plate splines to provide smooth mappings of the geographic representation of the sampling stations into their MDS representation. The composition of this mapping f and a monotone function g derived from MDS yields a nonparametric estimator of var(Z(x(a), t) - Z(x(b), t)) for any two geographic locations x(a) and x(b) (monitored or not) of the form g(\f(x(a)) - f(x(b))\). By restricting the monotone function g to a class of conditionally nonpositive definite variogram functions, we ensure that the resulting nonparametric model corresponds to a nonnegative definite covariance model. We use biorthogonal grids, introduced by Bookstein in the field of morphometrics, to depict the thin-plate spline mappings that embody the nature of the anisotropy and nonstationarity in the sample covariance matrix. An analysis of mesoscale variability in solar radiation monitored in southwestern British Columbia demonstrates this methodology.