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Modelling Longitudinal and Spatially Correlated Data pp 211–220Cite as

Bounded Influence Estimation in a Spatial Linear Mixed Model

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Part of the book series: Lecture Notes in Statistics ((LNS,volume 122))

Abstract

Kriging is an interpolation method that consists of finding a predictor linear function of the observations, minimizing the mean squared prediction error or kriging variance. Under multivariate normality assumptions, the given predictor is the best linear unbiased predictor, but if the underlying distribution is not normal, the estimator shall not be unbiased and shall be vulnerable to outliers. In the spatial context, it is not only the presence of outliers that may spoil the predictions, but also the boundary sites, usually corners, that tend to have high leverage. Therefore, kriging predictions are very sensitive on these corners, giving rise to values extremely vulnerable to small changes in the data. To overcome this situation, a spatial linear mixed model is proposed, deriving a bounded influence estimator of the location parameters. To illustrate the results, an application to Davis topographic data is presented.

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Author information

Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa Universidad Pública, Navarra

    Ana F. Militino & M. Dolores Ugarte

  2. Universidad Pública de Navarra, Campus Arrosadía, 31006, Pamplona, Spain

    M. Dolores Ugarte

Authors
  1. Ana F. Militino
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  2. M. Dolores Ugarte
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Editor information

Editors and Affiliations

  1. Department of Forestry, Virginia Polytechnic University and State Institute, Blacksburg, VA, 24061-0324, USA

    Timothy G. Gregoire

  2. Department of Statistics, University of California, Berkeley, Berkeley, CA, 94720, USA

    David R. Brillinger

  3. Department of Mathematics and Statistics, University of Lancaster, Lancaster, LA1 4YF, England

    Peter J. Diggle

  4. Department of Animal Sciences, University of Maryland, College Park, College Park, MD, 20742-2311, USA

    Estelle Russek-Cohen

  5. Department of Fisheries and Oceans, P.O. Box 5567, St. John’s, Newfoundland, A1C 5X1, Canada

    William G. Warren

  6. SAS Campus Drive, SAS Institute Inc., Cary, NC, 27513-2414, USA

    Russell D. Wolfinger

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© 1997 Springer Science+Business Media New York

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Militino, A.F., Ugarte, M.D. (1997). Bounded Influence Estimation in a Spatial Linear Mixed Model. In: Gregoire, T.G., Brillinger, D.R., Diggle, P.J., Russek-Cohen, E., Warren, W.G., Wolfinger, R.D. (eds) Modelling Longitudinal and Spatially Correlated Data. Lecture Notes in Statistics, vol 122. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0699-6_18

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  • DOI: https://doi.org/10.1007/978-1-4612-0699-6_18

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98216-8

  • Online ISBN: 978-1-4612-0699-6

  • eBook Packages: Springer Book Archive

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