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[ai-geostats] the sum of the simple kriging weights

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  • Andreas Dominik Cullmann
    Hi all, the simple kriging weights do not sum to a constant. From Olea (1999): Geostatistics for engineers and earth scientists , Kluwer, Boston, p.60: (c)
    Message 1 of 2 , Jan 4, 2005
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      Hi all,
      the simple kriging weights do not sum to a constant.

      From Olea (1999): 'Geostatistics for engineers and earth scientists',
      Kluwer, Boston, p.60:
      '(c) The possibility of having negative weights implies that the
      estimate is not confined to the data interval;...'

      To me, this sounds like if the sum of the simple kriging weights
      is resticted to some interval, especially since I've never seen
      any sum of weights not in [0,1].
      Does anybody know any hint, evidence or proof of such a
      restriction?

      Thanks a lot.


      ---------------------------------
      Andreas Dominik Cullmann
      Institut fuer forstliche Biometrie und Informatik
      Buesgenweg 4
      37077 Goettingen
      Germany
      Tel: ++49-551-39-3462
    • Colin Daly
      AndreasThere is no restriction - although in most cases the values will lie beteween 0 and 1. In principle the weights can sum to anything - the value
      Message 2 of 2 , Jan 4, 2005
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        RE: [ai-geostats] the sum of the simple kriging weights

        Andreas

         There is no restriction - although in most cases the values will lie beteween 0 and 1. In principle the weights can sum to anything - the value (1-sum_of_weights) is the weight associated to the global mean value. If all your data are very far from the point to be estimated - and the variogram range is short, then the weight on the mean will be close to 1 (so that the sum of weights on the data will be near zero)

         With a 'quirky' variogram such as the gaussian, you can construct scenarios ( perhaps using the screen effect) where the sum of weights is outside the [0,1] interval.

         If you have a math background - then simple kriging is the unrestricted projection of the random variable at the point you are trying to estimate onto the linear space generated by the known data using the covariance as scalar product. (This would convince you that there are no restrictions on the weights)

        Regards

        Colin Daly

        -----Original Message-----
        From:   Andreas Dominik Cullmann [mailto:acullma@...]
        Sent:   Tue 1/4/2005 3:02 PM
        To:     ai-geostats@...
        Cc:    
        Subject:        [ai-geostats] the sum of the simple kriging weights
        Hi all,
        the simple kriging weights do not sum to a constant.

        From Olea (1999): 'Geostatistics for engineers and earth scientists',
        Kluwer, Boston, p.60:
        '(c) The possibility of having negative weights implies that the
        estimate is not confined to the data interval;...'

        To me, this sounds like if the sum of the simple kriging weights
        is resticted to some interval, especially since I've never seen
        any sum of weights not in [0,1].
        Does anybody know any hint, evidence or proof of such a
        restriction?

        Thanks a lot.


        ---------------------------------
        Andreas Dominik Cullmann
         Institut fuer forstliche Biometrie und Informatik
         Buesgenweg 4
         37077 Goettingen
         Germany
         Tel: ++49-551-39-3462



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