[R-sig-Geo] Cokriging unbiasedness condition

[Edzer Pebesma]

That book is very good, but contains some first signs of black magic.

I would recommend Don Myers' "Matrix formulation of cokriging", Jay Ver
Hoef and Noel Cressie's "Multivariable spatial prediction", but in
particular Hans Wackernagel's book on multivariate geostatistics to
learn more.

On 04/06/2011 05:09 PM, Piero Campalani wrote:
> Well, I am asking this because in "An Introduction to Applied
> Geostatistics", §17, they point out how these that are meant as "usual
> nonbias conditions" are not believed to be the best ones, though they are
> the most commonly used..
> Using just one nonbias condition involving all the cokriging coefficients
> instead, would bring improvements in the estimation process, at the cost of
> a little change in the estimator (that should include estimated means of the
> involved variables to effectively ensure unbiasedness).
> 
> I may have misunderstood however, or these may not be general statements but
> rather case-specific conclusions.. !
> 
> Regards,
> Piero
> 
> On 6 April 2011 17:00, Edzer Pebesma <edzer.pebesma at uni-muenster.de> wrote:
> 
>> With the usual ones I refered to (what I believe is) ordinary cokriging:
>> each variable has sum of weights for the variable itself is 1, sum of
>> the weights for all other variables is 0.
>>
>> On 04/06/2011 01:59 PM, Piero Campalani wrote:
>>> Thank you.
>>> So that means that e.g. with ordinary cokriging, the one condition "sum
>> of
>>> all coefficients equal 1" is used, and not e.g. the (n+1) nonbias
>> conditions
>>> by which the coefficients of the target variable sum to 1, whereas the
>>> coefficients of the n secondary variables sum to 0 ?
>>> I'm sorry, I'm not aware of what the "usual ones" are unluckily. :)
>>>
>>> Regards.
>>>
>>> On 6 April 2011 13:02, Edzer Pebesma <edzer.pebesma at uni-muenster.de>
>> wrote:
>>>
>>>>
>>>>
>>>> On 04/06/2011 11:43 AM, piero campa wrote:
>>>>> Dear list and dear Edzer,
>>>>> I was wondering which unbiasedness condition(s) is/are used in the
>>>>> predict.gstat function when cokriging methods are called.
>>>>
>>>> The usual ones; if no trend function is specified (...~1), then an
>>>> unbiasedness condition for the mean value is used; if some trend
>>>> function is specified the conditions extend to the mean parameters.
>>>>
>>>> Function gstat() has a merge parameter that allows one to join the
>>>> unbiasedness condition for any two parameters to one.
>>>>>
>>>>> Thank you in advance.
>>>>> /Piero
>>>>>
>>>>> --
>>>>> View this message in context:
>>>>
>> http://r-sig-geo.2731867.n2.nabble.com/Cokriging-unbiasedness-condition-tp6245350p6245350.html
>>>>> Sent from the R-sig-geo mailing list archive at Nabble.com.
>>>>>
>>>>> _______________________________________________
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>>>>
>>>> --
>>>> Edzer Pebesma
>>>> Institute for Geoinformatics (ifgi), University of Münster
>>>> Weseler Straße 253, 48151 Münster, Germany. Phone: +49 251
>>>> 8333081, Fax: +49 251 8339763  http://ifgi.uni-muenster.de
>>>> http://www.52north.org/geostatistics      e.pebesma at wwu.de
>>>>
>>>> _______________________________________________
>>>> R-sig-Geo mailing list
>>>> R-sig-Geo at r-project.org
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>>>>
>>>
>>
>> --
>> Edzer Pebesma
>> Institute for Geoinformatics (ifgi), University of Münster
>> Weseler Straße 253, 48151 Münster, Germany. Phone: +49 251
>> 8333081, Fax: +49 251 8339763  http://ifgi.uni-muenster.de
>> http://www.52north.org/geostatistics      e.pebesma at wwu.de
>>
> 

-- 
Edzer Pebesma
Institute for Geoinformatics (ifgi), University of Münster
Weseler Straße 253, 48151 Münster, Germany. Phone: +49 251
8333081, Fax: +49 251 8339763  http://ifgi.uni-muenster.de
http://www.52north.org/geostatistics      e.pebesma at wwu.de