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GEOSTATS: Variogram and Weight matrix in regression.

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  • Marcel Nzeukou
    Hi everyone, I am interested in investigating the possible relationship between a VARIOGRAM and a WEIGHT MATRIX as both concepts are used to correct for a
    Message 1 of 5 , Nov 10, 1998
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      Hi everyone,

      I am interested in investigating the possible relationship between a
      VARIOGRAM and a WEIGHT MATRIX as both concepts are used to correct for a
      possible spatial pattern in the regression of a geographically referenced
      data set.
      I will be very grateful for help on any reference about any previous work
      done on this subject or any suggestion.

      Marcel Nzeukou
      U. of Arizona
      Dpt. of Mathematics


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    • John Kern
      Marcel and others, For situations where one is interested in a linear model Z=XB+resids, if the residuals are assumed to be from a stationary random function,
      Message 2 of 5 , Nov 10, 1998
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        Marcel and others,

        For situations where one is interested in a linear model Z=XB+resids, if the
        residuals are assumed to be from a stationary random function, then the
        weight matrix is simply the spatial covariance matrix for the residuals.
        Further, under stationarity, we have a one to one relationship between the
        variogram and covariance function so it is a fairly straight forward step.
        We can estimate the covariance function parameters by restricted maximum
        likelihood followed by refinement of the regression parameters as
        Generalized least squares estimates. These are the BLUE estimators under the
        second order stationarity assumption.

        Interesting research questions probably arrise in handling non-stationarity
        in the covariance function. As question I am wonderingif this is taken care
        of using intrinsic random function models. Anyone?

        See Cressie 1990 for this development under universal kriging and
        generalized linear models.


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      • Wulder, Mike
        Greetings, Concerning landform classifications from DEM data. Dr. Phil Giles undertook a number of studies to generate geomorphological signatures from slope
        Message 3 of 5 , Nov 10, 1998
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          Greetings,

          Concerning landform classifications from DEM data.

          Dr. Phil Giles undertook a number of studies to generate geomorphological
          signatures from slope units computed from DEMs. An example of this work
          is:

          Giles, P. T., 1998; Geomorphological Signatures: Classification of
          Aggregated Slope Unit Objects from Digital Elevation and Remote Sensing
          Data, Earth surface processes and landforms, v 23 n 7, pp. 581-

          Best regards...Mike

          > ----------
          > From: Eric Pirard[SMTP:eric.pirard@...]
          > Sent: November 10, 1998 6:38 AM
          > To: ai-geostats@...
          > Subject: Re: GEOSTATS: topography & modelling
          >
          > Hello Umberto,
          >
          > I have no knowledge of previous attempts of this kind to analyze DEMs and
          > classify landforms. My experience with topography is more at microscopical
          > level (surfometry).
          > I would like to draw your attention on the potential of mathematical
          > morphology to tackle the problem of analysis of landforms. Basic tools
          > such as Opening / Closing and other subsequent classification tools such
          > as Watersheds and Tophats are designed to tackle the problems you want to
          > solve.
          > I had experience of using fractal dimensions, Fourier transforms and
          > Mathematical Morphology in the analysis of roughness and found that Morpho
          > Math is the most sensitive and most robust tool for such work.
          > In any case, you should not neglect the literature on surface topography
          > in tribology (mechanics) and in grey level image analysis. These
          > disciplines are much closer to your work than you might expect.
          > Basically, this cross disciplinary need is the reason why we are
          > organising GEOVISION 99 in Liege. I hope to welcome you there.
          >
          > The second circular is no available from :
          >
          > http://www.lgih.ulg.ac.be/geovision/circular2/circular2.htm
          >
          >
          > Best regards and greetings from Enrico BONINO
          >
          >
          >
          > Prof. Eric PIRARD /.
          > Universite de Liege
          > ---- MICA ----
          > Caracterisation des Matieres Minerales Naturelles
          > Avenue des Tilleuls, 45
          > 4000 LIEGE
          > BELGIUM
          >
          > Tel.: +32-4-366.95.28. FAX: +32-4-366.95.20. e-mail :
          > Eric.Pirard@...
          > http://www.ulg.ac.be/mica
          > Join us at GEOVISION '99 ... http://www.lgih.ulg.ac.be/geovision -- *To
          > post a message to the list, send it to ai-geostats@.... *As a
          > general service to list users, please remember to post a summary of any
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          >
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