Cross-validation is carried out in order to select the theoretical variogram model better fitting the experimental one. Practically, when you use some empirical models such as Exponential Guassein etc.. its better to use cross validation in order to compare results. In my opinion you can use all of your desired statistical parameters. for example you can assume the mean of normalised residuals (ME) and the variance of normalised residuals (VE) but note that the model having the closest value of ME to zero, and VE closest to 1 is the one best fitting the experimental variogram. In this way you can have a good comparison in order to check the performance of your kriging interpolation values. 

Can you explain more for me how you could evaluate sill range and nugget parameters in your work?

Thanks Ardalan Malekzadeh , for you reply. How can I understand, what statistical parameter I should calculate? And could you please give the formula of ME and VE?

 I am attaching my R code for 1 hour to show you how I evaluated variogram parameters. If you have further question, please let me know.

I think Its very simple for you because you used some similar statistical parameters before in your calculations. Actually when you want to leave out one point from your data set it means that you want to have comparison between real and predicted values in that point. Hence you must evaluate in this way :

1-Calculate differences between your real and predicted values.

2-Normalizing these differences.

3-Calculate mean and variance of these normalized differences.

Finally, you have ME and VE parameters.

Sorry .how to normalize these residual?

did you mean,  ME=mean[(predicted value- observed value)/observed value] ?

How did you normalized Mean Normalized Bias (MNB) parameter in your work?

Absolutely you used normalization action in order to evaluate this parameter, don't you?

could you answer my question firstly?

Actually I am not sure! After cross-validation, I got observed values and predicted values dataset. Then to calculate MNB ,I used the following formula (which I got from a paper),

MNB = mean((predicted values-observed values)/observed values)*100%

Is this wrong way to calculate MNB?

Actually, I don't have any Ideas for MNB calculation.

But you can see this link in statistics in order to normalize your desired residuals.

https://en.wikipedia.org/wiki/Normalization_(statistics)

Kind Regards.

It is not as simplistic as just looking at the values of a few statistics, You need to also look at how sensitive those values are to changing the variogram model type, variogram parameter(s) and search neighborhood parameters.

The problem with normalizing by the observed value is that you do not have an expected value to compare with (you would not be able to compute the expected value of the normalized difference without knowing the multivariate distribution of the quotients.

In the case of Simple kriging (as opposed to Ordinary kriging), the correlation of the observed to predicted is theoretically one but in the case of Ordinary kriging the theoretical correlation is less than one because of the Lagrange multipliers.

Since the Ordinary kriging estimator is unbiased, the theoretical mean error is zero but the empirical mean error should be compared to the scale of the data. If all the data values are in the range 1000 to 5000 then an empirical mean error of 50 is still pretty small but if the data values are in the range of  1 to 5 then an empirical mean error of 0.1 is moderately large

A better choice to normalize the prediction errors is to use the kriging standard deviation (note that it does not depend on the data values) and it is not an "estimated" value, i.e. it is not a sample standard deviation.

Using  THIS normalization, the RMSE expected value is one (actually it is the MSE that has an expected value of one.

Make a plot of the data locations and code each data location with the prediction error , alternatively the normalized prediction error.  Using Chebyshev's Inequality, the fraction of normalized prediction errors exceeding 2.5 should be less than 0.05

The cross validation statistics are useful to examine the data for oultiers or other "unusual" data values or possible violations of the stationarity assumption

See

1991, Myers,D.E., On Variogram Estimation in Proceedings of the First Inter. Conf. Stat. Comp., Cesme, Turkey, 30 Mar.-2 April 1987, Vol II, American Sciences Press, 261-281

Thank you very much Donald Myers.

could you please explain agin, what did you mean by ,"the fraction of normalized prediction errors exceeding 2.5 should be less than 0.05"?

Fraction between which parameters?

This is based on the use of Chebyshev's Inequality. The validity of this inequality does not depend on any distributional assumptions but it does depend on the fact that the Ordinary kriging estimator is unbiased and hence that the expected prediction error is zero.