# [R-sig-Geo] Cokriging unbiasedness condition

Edzer Pebesma edzer.pebesma at uni-muenster.de
Wed Apr 6 21:04:57 CEST 2011

```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

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.
>>>>>
>>>>> /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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>>>>> 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
>>>>
>>>> _______________________________________________
>>>> R-sig-Geo mailing list
>>>> R-sig-Geo at r-project.org
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>>>>
>>>
>>
>> --
>> 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

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