Timeline for How to estimate confidence interval of a least-squares fit parameters by means of numerical Jacobian
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 1, 2017 at 22:28 | vote | accept | MarcinKonowalczyk | ||
| Mar 1, 2017 at 22:27 | history | bounty ended | MarcinKonowalczyk | ||
| Feb 28, 2017 at 19:41 | comment | added | Bill | For myself, when I estimate a model with multiple local maxima, I spend some effort to try to find the global maximum (though this is difficult to ensure, of course). My intuition is that the global maximum will have better small sample properties. I don't know of a proof for this, though. | |
| Feb 28, 2017 at 19:34 | comment | added | Bill | Basically, the answer to your other question is no. It does not matter if you have not obtained the global minimum. But the reason this is true might bother you. To get the estimator $P'$ to be consistent for the true value of the parameter, you need your objective function (times $1/N$) to converge to a function with a unique minimum on the interior of the feasible set of parameter values. So, as $N$ goes to infinity, there is only one solution to the first order condition, eventually. So, the whole local/global problem goes away in the limit. | |
| Feb 28, 2017 at 18:58 | comment | added | Bill | Yes, you should use $H=J^T_f J_f$. It would not make sense to divide by $N$. This would cause the variance matrix to converge to something positive-definite (usually). That makes no sense. The variance is going to go to zero as $N$ goes to infinity, assuming some regularity conditions. | |
| Feb 28, 2017 at 17:45 | vote | accept | MarcinKonowalczyk | ||
| Mar 1, 2017 at 22:28 | |||||
| Feb 28, 2017 at 10:42 | comment | added | MarcinKonowalczyk | Also; would this procedure still work if you did not assume that the global minimum has been reached? | |
| Feb 28, 2017 at 10:36 | comment | added | MarcinKonowalczyk | Thank you, that is very helpful. It does not actually answer all my questions though. Given all your assumptions about my problem (which are basically correct), can I use the $H≈J^T_fJ_f$ estimate for $H$? Would it make sense to use $H≈\frac1NJ^T_fJ_f$? | |
| Feb 27, 2017 at 21:12 | history | answered | Bill | CC BY-SA 3.0 |