- Apr 3, 2000Hello,

The main difference between the Error Variance (EV) and

Micro Variance (MV) is that MV=0 for h=0 and not EV.

Thus, whenever h>0 both components are incorporated

into the computation of the nugget effect.

I am not surprised that you get similar estimates

(at unsampled locations) if you use the same NE

since the repartition of the nugget variance between

Error Variance and Micro Variance won't impact the

computation of the covariance values in your kriging

system except for the diagonal of the left-hand-side

kriging matrix. At sampled locations though the two

systems will yield different estimates.

The relative importance of the two components can be quantified

if you have collected information about measurement errors

(e.g. through duplicates or triplicates): many examples can

be found in the soil science literature. An alternative is to look

at the nugget effect of the cross variogram between two

variables which, under the assumption that measurement errors

of two variables are uncorrelated, can help the interpretation of

the nugget effect of the two direct variograms (non-zero nugget

effect on the cross variogram is due to micro-scale variation

common to both variables), see my book. p. 102-103

and the reference:

Goovaerts, P. and R. Webster. 1994.

Scale-dependent correlation between topsoil copper and cobalt

concentrations in Scotland.

European Journal of Soil Science, 45(1):79--95.

Cheers,

Pierre

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________ ________

| \ / | Pierre Goovaerts

|_ \ / _| Assistant professor

__|________\/________|__ Dept of Civil & Environmental Engineering

| | The University of Michigan

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On 2 Apr 2000, Gregoire Dubois wrote:

> Dear all,

>

> I have two questions.

>

> The first one is about the use of cross-validation, jacknife and bootstrap in

> geostatistics while developed for independent and identically distributed

> observations. What are the consequences of the application of these techniques

> to dependent data and what can be done to adapt these techniques to

> geostatistics.

>

> My second question is about the nugget effect, which can be defined as

>

> Nugget Effect (NE) = Error Variance (EV) + Micro Variance (MV) ,

>

> where the error variance is the variance of the measurement errors, and the

> micro variance is the variance of the small scale structure.

>

> This definition is the one implemented in Surfer and follows the

> recommendation of Cressie

>

> CRESSIE N. (1993)

> Statistics for spatial data

> John Wiley & Sons Inc. (Revised Edition)

> (see pages 127 - 130)

>

> When EV = 0 and NE > 0, the estimates will honor every observation, when MV =

> 0 and NE > 0, the estimates do not honor every observation. Both situations

> will have a smoothing effect.

>

> I have made a few tests to evaluate the relative impact of both components but

> could not see differences between EV and MV. For a given value of the NE and

> for different combinations of EV and MV, I always get the same estimates. Does

> anyone have an explanation for that ?

>

> I couldn't find any references to publications where both components are

> quantified in a case study and would welcome any suggestions.

>

> Thank you for any help

>

> Gregoire

>

>

>

> Gregoire Dubois

> Section of Earth Sciences

> Institute of Mineralogy and Petrography

> University of Lausanne

> Switzerland

>

> Currently detached in Italy

>

> http://curie.ei.jrc.it/ai-geostats.htm

>

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