Spatial design matrices and associated quadratic forms: structure and properties

Grant Hillier and Federico Martellosio ()

Journal of Multivariate Analysis, 2006, vol. 97, issue 1, 1-18

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.

Keywords: Cumulant; Intrinsically; stationary; process; Kronecker; product; Quadratic; form; Spatial; design; matrix; Variogram (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (2)

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Related works:
Working Paper: Spatial design matrices and associated quadratic forms: structure and properties (2006)
Working Paper: Spatial design matrices and associated quadratic forms: structure and properties (2004)
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