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Spatial design matrices and associated quadratic forms: structure and properties

Hillier, G and Martellosio, F Spatial design matrices and associated quadratic forms: structure and properties .

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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.

Item Type: Other
Authors :
NameEmailORCID
Hillier, GUNSPECIFIEDUNSPECIFIED
Martellosio, Ff.martellosio@surrey.ac.ukUNSPECIFIED
Uncontrolled Keywords : Cumulant, Intrinsically Stationary Process, Kronecker
Depositing User : Symplectic Elements
Date Deposited : 16 May 2017 15:14
Last Modified : 17 May 2017 14:33
URI: http://epubs.surrey.ac.uk/id/eprint/818254

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