The excellent lmfit package lets one to run nonlinear regression. It can report two different conf intervals - one based on the covarience matrix the other using a more sophisticated tecnique based on an F-test. Details can be found on the doc. I would like to understand he reasoning behind this technique in depth. Which topics should i read about? Note: i have sufficient stats knowledge
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F stats and other associated methods for obtaining confidence intervals are far superior to a simple estimation of te co variance matrix for non-linear models (and others).
The primary reason for this is the lack of assumptions about the Gaussian nature of error when using these methods. For non-linear systems, confidence intervals can (they don't have to be) be asymmetric. This means that the parameter value can effect the error surface differently and therefore the one, two, or three sigma limits have different magnitudes in either direction from the best fit.
The analytical ultracentrifugation community has excellent articles involving error analysis (Tom Laue, John J. Correia, Jim Cole, Peter Schuck are some good names for article searches). If you want a good general read about proper error analysis, check out this article by Michael Johnson: http://www.researchgate.net/profile/Michael_Johnson53/publication/5881059_Nonlinear_least-squares_fitting_methods/links/0deec534d0d97a13a8000000.pdf