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

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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)
Message 1 of 2 , Jan 4, 2005
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
• 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
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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