How to estimate the parameters of the variable from which we make draws in MSLE. For example, Consider (example from Cameron and Trivedi-12.4.5 Unobserved heterogeneity) $$ y_i=\theta +u_i+\epsilon$$
I am interested in getting value of theta to get that I use MSLE. For using MSLE we make draws from u but how do I approach the problem if I don't know the parameters of u.
Meaning if I know the distribution of u but it has unknown parameter how do I get theta and parameters of u?