I have many curves that I want to fit using a convolution of some functions. These functions include Weibull distributions with 2 parameters
k, as well as a function
B(t) such as
measured curves to fit to model = F(lambda1, k1, kambda2, k2) + B(t)
The main problem here is that even if the lambda's, k's and B are not colinear, they can be "kind of" substituted and the optimization can lead to different local minima, with a close final error, but parameters not close at all.
This is a problem because I intend to interpret the value of these parameters as natural characteristics of the objects I observe.
Our actual approach is to minimize the number of parameters, i.e. fixing some of the lambda's and k's, as we would do if there were a function linking them. However this is arbitrary + this is a sacrifice as I can not interpret this parameters value anymore.
So question : is there a method / analysis / related problem / science paper dealing with this problem of unstable optimization when parameters are not exactly perpendicular degrees of liberty ?