Spatial design matrices and associated quadratic forms: structure and properties
Spatial design matrices and associated quadratic forms: structure and properties
The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices. These are the matrices implicitly defined by quadratic forms that arise naturally in modelling intrinsically stationary and isotropic spatial processes. We give concise structural formulae for these matrices, and simple generating functions for them. The generating functions provide formulae for the cumulants of the quadratic forms of interest when the process is Gaussian, second-order stationary and isotropic. We use these to study the statistical properties of the associated quadratic forms, in particular those of the classical variogram estimator, under several assumptions about the actual variogram.
cumulant, intrinsically stationary process, kronecker product, quadratic form, spatial design matrix, variogram
1-18
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1
Martellosio, Federico
4fa40068-a4be-4f23-be6f-83cbdc33685b
2006
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1
Martellosio, Federico
4fa40068-a4be-4f23-be6f-83cbdc33685b
Hillier, Grant and Martellosio, Federico
(2006)
Spatial design matrices and associated quadratic forms: structure and properties.
Journal of Multivariate Analysis, 97 (1), .
(doi:10.1016/j.jmva.2004.11.004).
Abstract
The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices. These are the matrices implicitly defined by quadratic forms that arise naturally in modelling intrinsically stationary and isotropic spatial processes. We give concise structural formulae for these matrices, and simple generating functions for them. The generating functions provide formulae for the cumulants of the quadratic forms of interest when the process is Gaussian, second-order stationary and isotropic. We use these to study the statistical properties of the associated quadratic forms, in particular those of the classical variogram estimator, under several assumptions about the actual variogram.
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Published date: 2006
Keywords:
cumulant, intrinsically stationary process, kronecker product, quadratic form, spatial design matrix, variogram
Identifiers
Local EPrints ID: 34566
URI: http://eprints.soton.ac.uk/id/eprint/34566
ISSN: 0047-259X
PURE UUID: 995d4fae-ac1a-41c1-8f3f-1102e74a61ed
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Date deposited: 16 May 2006
Last modified: 16 Mar 2024 02:42
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Author:
Federico Martellosio
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