Spatial design matrices and associated quadratic forms: Structure and properties
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.
Year of publication: |
2004
|
---|---|
Authors: | Hillier, Grant ; Martellosio, Federico |
Publisher: |
London : Centre for Microdata Methods and Practice (cemmap) |
Subject: | Cumulant , Intrinsically Stationary Process , Kronecker Product , Quadratic Form , Spatial Design Matrix , Variogram |
Saved in:
freely available
Series: | cemmap working paper ; CWP16/04 |
---|---|
Type of publication: | Book / Working Paper |
Type of publication (narrower categories): | Working Paper |
Language: | English |
Other identifiers: | 10.1920/wp.cem.2004.1604 [DOI] 474489353 [GVK] hdl:10419/79307 [Handle] RePEc:ifs:cemmap:16/04 [RePEc] |
Source: |
Persistent link: https://www.econbiz.de/10010318484
Saved in favorites
Similar items by person
-
Properties of the maximum likelihood estimator in spatial autoregressive models
Hillier, Grant, (2013)
-
Spatial circular matrices, with applications
Hillier, Grant, (2010)
-
Spatial circular matrices, with applications
Hillier, Grant H., (2010)
- More ...