Eigenstructures of spatial design matrices

David J. Gorsich,Marc G. Genton,Gilbert Strang

Journal of Multivariate Analysis（2002）

引用 18|浏览1

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摘要

In estimating the variogram of a spatial stochastic process, we use a spatial design matrix. This matrix is the key to Matheron's variogram estimator. We show how the structure of the matrix for any dimension is based on the one-dimensional spatial design matrix, and we compute explicit eigenvalues and eigenvectors for all dimensions. This design matrix involves Kronecker products of second order finite difference matrices, with cosine eigenvectors and eigenvalues. Using the eigenvalues of the spatial design matrix, the statistics of Matheron's variogram estimator are determined. Finally, a small simulation study is performed.

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关键词

spatial statistics,order finite difference matrix,small simulation study,discrete cosine transform,spatial design matrix,kriging,kronecker product,design matrix,variogram,eigenvalue,one-dimensional spatial design matrix,variogram estimator,cosine eigenvectors,eigenvector,explicit eigenvalues,spatial stochastic process,matheron's estimator,eigenvalues,eigenvalues and eigenvectors,finite difference,eigenvectors,stochastic process,second order

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