Spatial design matrices and associated quadratic forms: structure and properties

Hillier, Grant and Martellosio, Federico (2006): Spatial design matrices and associated quadratic forms: structure and properties. Published in: Journal of Multivariate Analysis , Vol. 97, (2006): pp. 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cumulant; Intrinsically stationary process; Kronecker product; Quadratic form; Spatial design matrix; Variogram
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C31 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions ; Social Interaction Models; C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics

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