On dealing with spatially correlated residuals in remote sensing and GIS

Nicholas A.S. Hamm, Nicholas A.S. Atkinson, Edward J. Milton

Research output: Chapter in Book/Conference proceedingConference contributionpeer-review

Abstract

Key assumptions in standard regression models are that the residuals are independent and identically distributed. These assumptions are often not met in practice. In particular, the issue of spatial correlation amongst the residuals has had limited attention in the remote sensing and GIS literature. This paper discusses approaches that use familiar authorized models to specify the covariance amongst the residuals. The model parameters were estimated using a maximum likelihood approach (ML or REML). The accuracy of the approach was investigated using simulated data and found to give accurate estimates of the error variance (σ2), although estimates of and range (a) and nugget component (s) were less accurate. The approach was found to be robust to choice of covariance function (exponential or spherical). The approach was then extended to deal with heteroskedastic residuals by incorporating a weighting component analogous to that used in weighted least squares. This was also shown to yield accurate results for σ2, a and s. Finally, possibilities for extending these approaches to prediction are considered.

Original languageEnglish
Title of host publicationProceedings of ACCURACY 2006 - 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences
EditorsMarco Painho, Mario Caetano
PublisherInstituto Geografica Portugues
Pages603-613
Number of pages11
ISBN (Electronic)9728867271, 9789728867270
Publication statusPublished - 2006
Externally publishedYes
Event7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, ACCURACY 2006 - Lisbon, Portugal
Duration: 5 Jul 20067 Jul 2006

Publication series

NameProceedings of ACCURACY 2006 - 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences

Conference

Conference7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, ACCURACY 2006
Country/TerritoryPortugal
CityLisbon
Period5/07/067/07/06

Keywords

  • Correlated residuals
  • GIS
  • Regression
  • Remote sensing
  • Variogram

ASJC Scopus subject areas

  • Geography, Planning and Development
  • General Environmental Science
  • Modelling and Simulation

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