It seems that you can extend this further to calculate a madogram
for each grid density (mean absolute difference). Different grid
densities, different radii, ergo different madogram shapes. Each madogram
may or may not show a range. The trick is to come up with a grid
density that would result in a radius that is more or less equivalent
to the range, to extract maximum interpolation data. Because the
grid is on equal spacing, the problem is finding a range to compare to,
and the only one available would be the global range of the data.
Regards,
Syed
>Overlay a grid on a 2D distribution of random variables Z(x,y) and
>assign all such variables to the nearest grid node. Then consider
>the distribution of F(i,j) = (ZMAX-ZMIN)(i,j) for any grid node with
>nearby data. For simplicity, assume that the original random variables
>are (locally) normally distributed and that all collected at any node
>have the same mean and standard deviation. What is the distribution
>of F?
>
>My reason for asking is that I am trying to automatically select
>a grid row and column spacing to use in grid-based surface modeling
>and one intuitive criteria is to get a "dense enough" grid that the
>largest ZMAX-ZMIN for any single grid node is small relative to the
>range of Z values in the input data set. (Well, intuitive to me.)
>Then I started wondering what I might conclude if the sampled mean
>plus a couple of standard deviations for the population of such node
>variables was small. And then I got confused.
>
>I am guessing that the distribution of F is standard problem in
>statistics when the data are normal: Given M samples from N(0,1),
>what is the distribution of Zmax-Zmin? But I don't have the right
>"standard" statistics book.
>
>Hmmm. Maybe I am gathering information about the nugget for a data
>set?
>
>Thanks,
>
>Steven Zoraster
>
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