ENH: robust default start_params in M-estimators, RLM, and CovM ?

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Assessment

Difficulty
5/5
Estimated time
Over a week
Newbie friendliness
25/100
Issue type
Feature
Clarity
Needs clarification
Activity status
Stale
Tech stack
python
Domain
data

Research direction

No files or tests are named. Start by reading the M-estimators, RLM, and CovM entry points and the related context in #9227, then compare robust and nonrobust starting parameters for monotone and redescending norms; completion requires an agreed default strategy, including whether CovMM should be included.

Written by the indexing model from the issue text.

Description

comp-robust design type-enh

context #9227 adding S- and MM-estimators

I thinking whether we should change the starting parameters in M-estimators to a robust estimate, currently for CovM.

For monotone norm, the minimum is unique, so only relevant in terms of faster result.
If there are very few outliers, then OLS, resp. np.cov, is a good starting point.

For redescending norms, starting with a nonrobust estimate will often lead to the wrong local optimum.
We could choose one of the starting points in DetS estimators for those.

However, after #9227 we will have RLMDetSMM as recommended alternative for redescending norms with multiple starting points.
MM has also the advantage of a default scale with higher breakdown point than HuberScale default tuning. (But RLM default scale is 'mad' (high breakdown point, low efficiency).

(CovMM is still unsure because I don't know how to compute tuning parameter to achieve specified efficiency)

undecided (for CovM I might default to ogk if a redescending norm is used)

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