I estimate the parameters of a model using NMinimize (Minimize the distance between empirical and theoretical moments). I was wondering if there is a way to measure the strength of the estimates, something like a condition number?
Any help is greatly appreciated.
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Ah sorry for that. The original problem is more complex. I try a simple case for illustration. So, for example I want to find the parameters (a1 and a2) of the function Yi=a1 logCi+a2 log Li. I have 10 numerical values of Yi predicted from another empirical model (from now on referred to as Yi (empirical)). I want my theoretical model above to replicate the empirical values of Yi(theoretical) as closely as possible. So, I use NMinimize to find a1 and a2 such that the distance between Yi(empirical) and Yi(theoretical) is minimum for given Ci and Li. I minimize the function Total[(Yi(theoretical)-Yi(empirical))^2].
NMinimize finds a1 and a2 for me, no problem there. Now I want to check the accuracy of the solution. Let's say the standard errors of a1 and a2, how changes in Ci and Li affect the values a1 and a2. Is there a way other than bootstrapping to find the s.e of a1 and a2 found by NMinimize?
Thank you very much for your help.
Have you tried NonlinearModelFit? It returns a FittedModel which has several properties that characterize the fit. See the "Details and Options" section of the NonlinearModelFit documentation.
Thanks for your response. I am not sure a NonlinearModelFit will work. What I am doing is something like method of moments. But I will try it.