multidimensional pem (trust-region-reflective with lsqnonlin)

I need detailed information about the algorithm used by pem in the multidimensional case. In particular I am using it with an idnlgrey model, with a multidimensional equation non linear in parameters. I am using the trust-region-reflective algorithm (as i have bounds) with the lsqnonlin estimator.

I'd like to obtain precise information on how the prediction error estimate is performed with this particular setting. Thank you

Answer 1

[Matt J]

Maybe this is what you are looking for,

http://www.mathworks.com/help/optim/ug/least-squares-model-fitting-algorithms.html#broz0i4

[maru]

Hi Matt, thanks, but I see from the documentation of pem http://www.mathworks.it/help/ident/ref/pem.html on section Algorithms that it optimizes a function that is "a function of the number of data samples and becomes more accurate for larger values of N". In fact, comparing the result that I obtain with nonlinear least squares curve fitting, the result is different (better).

Reading the code, it seems that the getErrorAndJacobian.m file is relevant, but I wasn't able to get how V : loss function (Ny-by-Ny matrix) is computed, and if it's different from the normal least squares.

Thank you

[Matt J]

I'm not going to guess why, without seeing how you ran each fit. However, it may be that the solutions are unstable or that there are multiple solutions. As a test, you could take the "better" fit and initialize the weaker performing method with that. See if that changes the result.