ENH: roadmap, overview robust

[josef-pkt]

roadmap for parts
#9133
#9148

I still don't have an overview and design for the desired module structure, especially where to put helper functions and model/estimation functions that are reused in several other parts.
We need to avoid circular imports and need some main modules for user access.

• robust_linear_model (current)
• resistant_linear_model
  • to include DetS, DetMM (user facing)
  • needs deterministic starting sets using robust mahalanobis, and start subset OLS
• scale (current, including Mscale w. fixed mean)
  • not clear yet, simultaneous estimation, mean-scale as in scale.Huber, or leave it to regression models
• covariance: scatter or covariance (at normal reference distribution)
  • to include ogk, tyler, m-estimator for cov and mean
  • to include here or separate: covDetMCD, covDetS
    • needs starting sets, ogk, ..., and rank and other covariances in stats
• exog-outlier weights, Mallows, ..., not clear whether and where to add this (e.g. reuse GLM with weights)
• multivariate linear model, eventually (user facing)
  • based on covariance but with mean model instead of constant means
• multivariate stats, pca, ..., not sure, large literature as application of robust cov/scatter
• nonlinear model, eventually, old experimental PR (user facing)
• GLM, poisson, ... (no idea about module name, no details yet)
• regularized, penalized versions of above, include alongside main unregularized models/estimators
• ...
• helper functions and classes
  • norms current
  • robust.tools: currently tuning parameter, efficiency, breakdown point for univariate
  • multivariate, cov tuning parameter ?
• api to collect user facing functions and classes
• other
  • more cov_types, e.g. h4 and HC, HAC
  • prior weights freq_weights and var_weights (one R package maybe MASS rlm has both, one at a time)
• ...

Currently I'm not clear where to put the "det" starting set helper code
If I want to put covdetmcd and covdetS in covariance, then I have to put all supporting code also in there to avoid circular imports:
Starting sets needs cov/scatter like ogk, ....
We need application specific iter functions to iterate in DetXxx classes.
Then DetXxx classes need to go into user facing module.

I don't know if lazy imports will be able to handle all the circular imports.