But the function you are dealing with is f(\theta) = g(H(X \mid \theta), X) which in general will not be continuous(ly differentiable) if H isn’t, even if g is.
Depending on how bad things are, stochastic (eg simulated annealing) or robust deterministic derivative-free optimization methods are used in these cases. See
What are people’s recommendations for a global optimizer? I’m trying to do simulated method of moments (choosing a set of parameters for an economic model to minimise the distance between model predictions and data) and have so far been using blackboxoptim. I find it somewhat unreliable: running exactly the same code on the same data I find sometimes the optimizer gives me a parameter choice that provides a close fit to the data, but sometimes it just seems to get stuck without converging). Any …
I work with non-linear models that need to be calibrated to match data moments. The setup is simple. I have a function that takes a set of parameters as input (for example, a vector of floats), solves the model, and returns a measure of the distance between the model-generated moments and the data moments. Typically there are more moments than parameters. Hence, I use some simple weighting function to summarize the differences between model and data moments into one float. The objective is to m…
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