Cokriging unbiasedness condition

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Cokriging unbiasedness condition

piero campa
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.

Thank you in advance.
/Piero
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Re: Cokriging unbiasedness condition

edzer


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.
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> 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      [hidden email]

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Re: Cokriging unbiasedness condition

piero campa
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 <[hidden email]> 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.
> >
> > _______________________________________________
> > R-sig-Geo mailing list
> > [hidden email]
> > 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      [hidden email]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>
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Re: Cokriging unbiasedness condition

edzer
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 <[hidden email]> 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.
>>>
>>> _______________________________________________
>>> R-sig-Geo mailing list
>>> [hidden email]
>>> 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      [hidden email]
>>
>> _______________________________________________
>> R-sig-Geo mailing list
>> [hidden email]
>> 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      [hidden email]

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Re: Cokriging unbiasedness condition

piero campa
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 <[hidden email]> 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 <[hidden email]>
> 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.
> >>>
> >>> _______________________________________________
> >>> R-sig-Geo mailing list
> >>> [hidden email]
> >>> 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      [hidden email]
> >>
> >> _______________________________________________
> >> R-sig-Geo mailing list
> >> [hidden email]
> >> 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      [hidden email]
>
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Re: Cokriging unbiasedness condition

edzer
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 <[hidden email]> 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 <[hidden email]>
>> 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.
>>>>>
>>>>> _______________________________________________
>>>>> R-sig-Geo mailing list
>>>>> [hidden email]
>>>>> 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      [hidden email]
>>>>
>>>> _______________________________________________
>>>> R-sig-Geo mailing list
>>>> [hidden email]
>>>> 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      [hidden email]
>>
>

--
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      [hidden email]

_______________________________________________
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Re: Cokriging unbiasedness condition

piero campa
Thanks for the precious suggestions.

On 6 April 2011 21:04, Edzer Pebesma <[hidden email]> wrote:

> 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 <[hidden email]>
> 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 <[hidden email]>
> >> 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.
> >>>>>
> >>>>> _______________________________________________
> >>>>> R-sig-Geo mailing list
> >>>>> [hidden email]
> >>>>> 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      [hidden email]
> >>>>
> >>>> _______________________________________________
> >>>> R-sig-Geo mailing list
> >>>> [hidden email]
> >>>> 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      [hidden email]
> >>
> >
>
> --
> 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      [hidden email]
>
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