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Spatial design matrices and associated quadratic forms: structure and properties

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Author Info
Hillier, Grant
Martellosio, Federico

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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.

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File URL: http://mpra.ub.uni-muenchen.de/15807/
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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 15807.

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Date of creation: 2006
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Handle: RePEc:pra:mprapa:15807

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Related research
Keywords: Cumulant; Intrinsically stationary process; Kronecker product; Quadratic form; Spatial design matrix; Variogram;

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Find related papers by JEL classification:
C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General
C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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  1. Gorsich, David J. & Genton, Marc G. & Strang, Gilbert, 2002. "Eigenstructures of Spatial Design Matrices," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 138-165, January. [Downloadable!] (restricted)
  2. Ali, Mukhtar M, 1987. "Durbin-Watson and Generalized Durbin-Watson Tests for Autocorrelations and Randomness," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(2), pages 195-203, April.
  3. Hillier, Grant, 2001. "THE DENSITY OF A QUADRATIC FORM IN A VECTOR UNIFORMLY DISTRIBUTED ON THE n-SPHERE," Econometric Theory, Cambridge University Press, vol. 17(01), pages 1-28, February. [Downloadable!]
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