All the above are extremum estimators. GEE is usually formalized as estimating equations. Besides this we can also have estimators that directly specify the estimating equations, with maybe no consistent objective function for a minimum. Examples are in robust estimation with estimating equations for mean and scale specified separately. Maybe feasible GLS would also be in this category as estimation method without the extra MLE interpretation.
Two points: The estimators like OLS, GLM, GEE, RLM solve the estimating equations directly without going through an objective function, OLS, GLM have a (Q)MLE interpretation, RLM is an M-estimator. Even in cases like robust estimators, we could cast them in a exactly identified GMM framework, however similar to FGLS, and GLM/LEF, they exploit asymptotic independence or independence in expectation of the mean and variance terms.
What's the hierarchical tree?
What is common? What is specific?
How can we structure the code with class hierarchies, mixins and function for best code reuse and flexibility?
(Finetuning and special casing can always be done on the lowest level, so that's not directly relevant for the overall structure.)
When or how do we combine different estimators in one model? (e.g. MLE and QMLE, MLE and GMM/OLS, MLE and M-estimator)
example: cov_type makes MLE into QMLE, OLS/WLS mixes MLE/QMLE and LS/GMM
Components differ whether we want
full model with everything
prediction and forecasting only (machine learning style)
inference only: hypothesis tests (although we are moving towards simplified model for this, e.g. contingency table, and weightstats)
Towards more generic estimator frameworks
All the above are extremum estimators. GEE is usually formalized as estimating equations. Besides this we can also have estimators that directly specify the estimating equations, with maybe no consistent objective function for a minimum. Examples are in robust estimation with estimating equations for mean and scale specified separately. Maybe feasible GLS would also be in this category as estimation method without the extra MLE interpretation. Two points: The estimators like OLS, GLM, GEE, RLM solve the estimating equations directly without going through an objective function, OLS, GLM have a (Q)MLE interpretation, RLM is an M-estimator. Even in cases like robust estimators, we could cast them in a exactly identified GMM framework, however similar to FGLS, and GLM/LEF, they exploit asymptotic independence or independence in expectation of the mean and variance terms.
What's the hierarchical tree? What is common? What is specific?
How can we structure the code with class hierarchies, mixins and function for best code reuse and flexibility? (Finetuning and special casing can always be done on the lowest level, so that's not directly relevant for the overall structure.)
When or how do we combine different estimators in one model? (e.g. MLE and QMLE, MLE and GMM/OLS, MLE and M-estimator) example:
cov_typemakes MLE into QMLE, OLS/WLS mixes MLE/QMLE and LS/GMMComponents differ whether we want