As LsqFit.jl only calculates the standard error by using the Jacobian at the best-fit position I thought I try to write a small package for determining the confidence interval by data exploration.
As I am no expert I just implemented a method using an F-test and a simple linescan to test each parameter. (correlation is not taken into account yet, but creating a map in parameter space should not be that hard)
As this package is at a very early stage I wanted to check if something like this is already out there.
I could find F-tests being applied for confidence interval estimation in an youtube video and by the python package lmfit, but I could not find a good paper for the procedure.
I am wondering if the F-test is even a valid approach. Maybe someone with a deeper knowledge in statistics can help me here.
Matlab for example provides confidence interval estimation based on the Wald test, log likelihood and bootstrapping. Maybe a Wald test would be a good option to implement as bootstrapping is already covered by Bootstrap.jl.