Dear Dr. Boogaart
Could you please direct me to the page(s) where Cressie (1993) quoted this
modified definition of variogram?
Thanks
Abedini
On Mon, 7 May 2007, Gerald van den Boogaart wrote:
Dear Dr. Abedini,
As far as I understand there are two different definitions of the variogram
around:
2\gamma(x,x)=Var(Y(x)-Y(x'))=VAR[Y(x)-m(x)-Y(x')+m(x')]
and
2\gamma(x,x)=E[(Y(x)-Y(x'))^2]=VAR[Y(x)-m(x)-Y(x')+m(x')]+ (m(x')-m(x))^2
and furthermore the second definition is often applied to
Y(x)=Z(x)-m(x)
which is than again numerically equal to the first definition (in any case).
All these definitions are equal as long as the field is intrinsically
stationary. And as most Textbooks are discussing the stationary case, both
definitions are used without contradiction.
However in the instationary case you get the difference you observed. Cressie
insisted in some publications (e.g. in his 1993 book) that the second
definition is the correct definition for several reasons.
Best regards,
Gerald
Am Samstag, 5. Mai 2007 10:20 schrieb M.J. Abedini:
Dear Colleagues
I would greatly appreciate it if someone could shed some light on the
following issue:
For a nonstationary random function, variogram is defined as:
2*\gamma(x,x')=VAR[Y(x)-m(x)-Y(x')+m(x')]
If one simplifies the right hand side, the whole equation becomes:
2*\gamma(x,x')=R(x,x)+R(x',x')-2*R(x,x')
In a number of textbook, relation between covariance and variogram is
written as:
2*\gamma(x,x')=R(x,x)+R(x',x')-2*R(x,x')+[m(x)-m(x')]^2
Am I missing something from this mathematical manipulation?
Thanks
Abedini
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