Hi RGaters,
Does anyone know how to modify the order in a sample to modify Kendall's tau value(s) ? Let me clarify what I am looking for. Consider that we have N realizations of K random variables. Each realizations of the group of K variables is independent from the other ones. Inside this realization, the K variables might be independent or not, we do not really care. They even can follow different distributions. The question is the following : from any sample (size N x K) that we call M, can I exchange the places of M[i_1,1] with M[i_2,1], M[i_3,2] with M[i_4,2] and so on, possibly coming back to the first column with an interative algorithm to finally obtain as a result a new (rearranged) sample M' where tau[1,2] = first wanted value, tau[1,3] = second wanted value, and so on, i.e. can I get rearranged data to get a desired tau-matrix. If yes, any algorithm to suggest ?
I used Cholesky method to do the same thing to reach a desired Pearson-correlation matrix, but I have to admit I'm facing a wall on this issue right now.
Any help is welcome !
Hi Geoffrey,
when I get it right, this is a matter of programming. When you have data matrices (M) with well-defined entries, and you want to rearrange the data, then the use of excel would be of the lowest knowledge and usability threshold...:
Here is the process: Put the matrizes (M) in the excel tables, add an extra column, where the new row indices are defined (for M'). Then go to the macro-programer, which you can find in the developmenter section (has to be activated in the option settings in the menu). This developmenter tool works with 'basic' script language. There you can define variables which represent new matrices (they are called arrays. Their definition is like: array = [[1, 2, 3 ], [1, 2, 3]] which would be a 2x3 matrix with entries 1 to 3 in each column. Hence, like in every other programming language you can program a loop, which runs a counter through all possible indices and then looks up an entry in the excel table. When you you write a simple condition into the loop like: "look at the column where you can find the new indices" -> take this integer, and write the corresponding dv-value at this position into a new array. This loop has to run over the compelte data table (eg. loop from 1 to 100, if you run this for 100 rows), there are easy ways to make this happen and you can find it easily in the web. After every value has been written into the new array, you say excel 'now again count from 1 to 100, and write the array in sequential order into the cells 1 to 100 - et voila.
Hope this helps,
Best René
Hi René,
Thanks for your answer, however, I work in practice with 100 000 * 10 (it's true that I did not mentioned this above) matrices that I want to rearrange this sample to reach a target kendall's tau matrix (as close as possible). It is not the kendall's tau matrix that I want to rearrange, it is the data which lead to this kendall's tau matrix. That'd be too easy :)
Considering this, there is absolutely no way that I try every possible combinations and see which one to choose. I need some intelligent trick such as Cholesky method to get correlate variables.
So basically, it's not only about programming skills, it's also about applied mathematics.
Best regards !
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