Computationally exploitable structure of covariance matrices and generalized convariance matrices in spatial models

DOI10.1080/00949658908811149zbMath0726.62162OpenAlexW2056842996MaRDI QIDQ3350594

Dale L. Zimmerman

Publication date: 1989

Published in: Journal of Statistical Computation and Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00949658908811149

zbMATH Keywords

krigingrandom field modelsmatrix inversionspatial covariancepatterned matricesintrinsic random functions of order k

Mathematics Subject Classification ID

Inference from spatial processes (62M30) Random fields; image analysis (62M40) Probabilistic methods, stochastic differential equations (65C99)

Related Items (19)

Strict Positive Definiteness of a Product of Covariance Functions ⋮ Large-scale stochastic linear inversion using hierarchical matrices. Illustrated with an application to crosswell tomography in seismic imaging ⋮ Sparse matrix tools for Gaussian models on lattices ⋮ Computationally efficient cholesky factorization of a covariance matrix with block toeplitz structure ⋮ On strict positive definiteness of product and product-sum covariance models ⋮ Spatio-temporal generalized complex covariance models based on convolution ⋮ Unnamed Item ⋮ Generating correlated gaussian random fields by orthogonal polynomial approximations to the square root of the covariance matrix ⋮ Fast cars ⋮ Kriging and spatial design accelerated by orders of magnitude: combining low-rank covariance approximations with FFT-techniques ⋮ Bayesian spectral modeling for multivariate spatial distributions of elemental concentrations in soil ⋮ Computationally efficient restricted maximum likelihood estimation of generalized covariance functions ⋮ Estimation of covariance parameters in Kriging via restricted maximum likelihood ⋮ Computationally efficient generation of Gaussian conditional simulations over regular sample grids ⋮ Efficient generation of conditional simulations by Chebyshev matrix polynomial approximations to the symmetric square root of the covariance matrix ⋮ Measures of parameter uncertainty in geostatistical estimation and geostatistical optimal design ⋮ Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models ⋮ Application of FFT-based algorithms for large-scale universal kriging problems ⋮ Hyperbolic cross designs for approximation of random fields

Cites Work

• Minimum-variance unbiased quadratic estimation of covariances of regionalized variables
• Maximum likelihood estimation of models for residual covariance in spatial regression
• Efficient inversion of Toeplitz-block Toeplitz matrix
• On the design of experiments under spatial correlation
• Statistical Analysis of Field Experiments Using Neighbouring Plots
• The intrinsic random functions and their applications
• An Algorithm for the Inversion of Finite Toeplitz Matrices
• Toeplitz Matrix Inversion: The Algorithm of W. F. Trench
• Block Toeplitz Matrix Inversion

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