What do you mean by nonlinear structure? Can you specify a little more because simulating data is pretty easy to do if you know a couple of tricks and just because something has a nonlinear structure doesn't necessarily make it harder to simulate.
Plus some people think different things when they say nonlinear structure.
I am studying about kernel PCA and PCA and want to see their performances by using simulated data. PCA is good to use with data that has linear covariance structure (e.g., multivariate normal distribution). But Kernel PCA is good to capture nonlinear structure (maybe nonlinear covariance structure).
i kinda agree with Dason in which it is not entirely clear to me about what you want to do... HOWEVER, my interpretation of what you want is to generate data with a certain covariance/correlation structure that you specify but which does not necessarily come from a multivariate normal distribution (in which case you would only need to specify sigma as your covariance matrix and you get your data with the correlation/covariance that you want)
if this is what you're going to do, there're two was i know you can do it. you can either use Todd Headrick's statistical simulation book using the power method for polynomial transformation or you can use copulas.
i think headrick provides some code for matlab so you can do that, whereas R uses copulas. i dont have matlab so i only know how to generate them in R
O-M-G!!! such an honour to share the same board thread with you, Dr.!!
you... wouldn't happen to have some sort of version of it in R lying around somewhere, right? it's not that i dont like copulas, but i read the book and i kinda liked it better because of the control it gives you over the moments of the distributions. unfortunately, Mathematica is out of my budget for the time being so, as most graduate students, i rely on open-source stuff...