Is it statistically correct using the Jacobian provided by lsqnonlin as input for nlparci to get parameter confidence intervals (CI's)?

I used the global optimization toolbox (multi-start, genetic algorithm, global search, pattern search) to estimate the parameters of a complex nonlinear model from the data. This works well. The tools listed above do not provide the Jacobian matrix. So, after finishing parameter optimization I run lsqnonlin with the previously optimized parameters (Nlinfit is not or less appropriate for the problem). As expected, the parameter estimates do not change. The Jacobian got as output from lsqnonlin is than used with nlparci to calculate the CI's. It works well, but are the estimated CI's statistically correct for the global optimization problem?

Johannes

Answer 1

[Star Strider]

I would think so, since lsqcurvefit is lsqnonlin optimised for curve fitting and its Jacobian and vector of residuals work with nlparci.