What is the formula used by nlparci?

Hello,

I used nlparci to give me the 95% confidence intervals of parameters I got from fitting data to a formula. That worked well, but I do not understand how it is computed.

I would like to know what formula is behind it.

Best regards

Answer 1

[Star Strider]

If you want to see the actual code:

edit('nlparci.m')

may allow you to see it. (I did not try that. Regardless, do not change any of the code!)

When I programmed nonlinear parameter estimation parameter confidence intervals (in FORTRAN, long before I knew about MATLAB), I did essentially the same as described in the Wikipedia article on Simple linear regression, using the approaches described by Beck and Arnold (Nonlinear Parameter Estimation in Engineering and Science, Wiley 1977). Also search on ‘nonlinear parameter estimation confidence intervals’ to find any number of relevant references.

[Icewind]

Well that answer helps me a bit. The wikipedia article gives a formula under confidence level - normality assumption. But the formula includes a t*_n-2 value which is not really clear to me what it means. I need an explanation/formula to include it in my masther thesis where I fitted some data. And I would like to explain how I got the confidence intervals. (I got them with nlparci from matlab, but that is probably not a really good explanation, so I wanted to give some explanation, just a few sentences)

[Star Strider]

Thank you.

See the Beck and Arnold reference for details, or other references that you can discover with an InterWeb search.

In my experience, nothing involving any statistical measure will ever be presented in ‘just a few sentences’! It is necessary to understand them in relevant detail, especially to explain them as part of your thesie defence!