Check and Extend statsmodels for pure Maximum Likelihood Estimators

Registered by joep

Currently every model is estimated with linear least squares or iterative least squares.

I would like to add models for which the main estimator is Maximum Likelihood, e.g. a multinomial logit

Where can this be added to the current model structure? What is the appropriate super class? How can we benefit from existing result statistics?

Expand current LikelihoodModel.newton method to calculate the common maximization, already in there fmin, but add availability of numerical or analytical scores (Jacobian) and Hessian as basis for estimation results.

This is also useful for MLE alternatives to existing estimators, e.g. GLSAR, and also for non-linear MLE, similar to scipy.interpolate.curve_fit but with all statistical results.

Proposed approach: get simple example to work with existing framework, then use it, eg. for a rewrite of mlogit_class.

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