how to generate pseudo-random positive definite matrix with constraints on the off-diagonal elements?

Question

The user wants to impose a unique, non-trivial, upper/lower bound on the correlation between every pair of variable in a var/covar matrix.

For example: I want a vari

Answer 1

Here is your response to my answer in the original thread:

"Come on people, there must be something simpler"

I'm sorry, but there is not. Wanting to win the lottery is not enough. Demanding that the Cubs win the series is not enough. Nor can you just demand a solution to a mathematical problem and suddenly find it is easy.

The problem of generating pseudo-random deviates with sample parameters in a specified range is non-trivial, at least if the deviates are to be truly pseudo-random in any sense. Depending on the range, one may be lucky. I suggested a rejection scheme, but also stated it was not likely to be a good solution. If there are many dimensions and tight ranges on the correlations, then the probability of success is poor. Also important is the sample size, as that will drive the sample variance of the resulting correlations.

If you truly want a solution, you need to sit down and specify your goal, clearly and exactly. Do you want a random sample with a nominal specified correlation structure, but strict bounds on the correlations? Will any sample correlation matrix that satisfies the bound on the aims be satisfactory? Are the variances also given?