Spatial design matrices and associated quadratic forms: structure and properties

Grant Hillier and Federico Martellosio

MPRA Paper from University Library of Munich, Germany

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)
JEL-codes: C01 C10 C31 (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (2)

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Related works:
Journal Article: 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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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:15807

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