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ENH: robust default start_params in M-estimators, RLM, and CovM ? #9243

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josef-pkt opened this issue May 10, 2024 · 0 comments
Open

ENH: robust default start_params in M-estimators, RLM, and CovM ? #9243

josef-pkt opened this issue May 10, 2024 · 0 comments

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@josef-pkt
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josef-pkt commented May 10, 2024

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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