[R-sig-Geo] Global variance estimation for evaluating resulting krigging quality

[Sébastien Durand]

Hello to all,

I have been trying to find the following since quite a while but I guess I was simply using the wrong terms to express myself.

The following shall describe what I am really looking for in R. 

I wish to know if there is an easy way to obtain that value using already preexisting functions. 

Considering the amount of function and package, I have a hard time thinking this has not been done yet!

Even so I have looked I am unable to find the proper function.

So to find the global variance of estimation here is the formula that need to be solved: 
 
1-	Global variance of estimation =  C(v,v) - lambda_v' * C(x,v)
	
	Where;
		C(v,v) is the mean of all covariances between the krigged points (a grid);
		lambda_v is the vector of weights used in the following global krigging:
		
2-		C(x,x) * lambda_v =  C(x,v)
	
	Where 
		C(x,x) is the covariance matrix of the initial points used (the last column and row are appended by 1 and end by a 0) 
			(these answer for the sum of weight constraint which must be equal to 1)
		C(x,v) is a vector of length equal to number of initial point feed to the krigging system, and contains for every initial point the covariance average between  all the krigged points. This vector is appended by the number 1 to all for the sum of weigth =1 constraint.

If any one is able to help me out... I will be a very very greatful
	
Sébastien