I am using the jacobianest function in order to evaluate the Jacobian and the confidence interval for my fitted parameters based on John D'Errico`s comment here: https://groups.google.com/forum/#!topic/comp.soft-sys.matlab/JJOqLCNJjF0
My problem that one a column of the Jacobian matrix has very small values (1e-29) and when I calculate Sigma which is proportional to inv(J'*J) (see the link above), I have a message:
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =5.516957e-117.
However, I have an excellent fit, the fitted parameters have a lot of sense but their error is so huge, it is totally unrealistic. I know that the approach above assumes that I have a Gaussian error system, but honestly, I do not know how I can be sure about it. I have a nonlinear equation with 15 parameters and I am using fminsearchcon to find the best fit with the least square method.
Is there a way to get a confidence interval using existing Matlab functions when the Gaussian assumption is not valid?
Every suggestion is welcome.
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