Review: cov_params, cov_type in RLM

[josef-pkt]

see also #4670
and issue for heteroscedasticity, correlation robust sandwiches.

I have again problems understanding what the cov_types in RLM actually do.

We need LATEX formulas, and get some ideas what how H1, H2, H3 differ

Salini et al have 5 cov_types in table 1.
It's for S-estimator, but locally they are the same as M-estimators

Salini, S., F. Laurini, G. Morelli, M. Riani, and A. Cerioli. 2022. “Covariance Matrices of S Robust Regression Estimators.” Journal of Statistical Computation and Simulation 92 (4): 724–47. https://doi.org/10.1080/00949655.2021.1972300.

main question would be how strongly inferential statistics like cov_params are influenced by outliers in exog, when X'X is not a good estimate for (expected or limiting) normalized_cov_params or hessian. Weights in current RLM are only for outliers in endog.

But that extension requires more background in outlier robust inference.
For basic cov_type: AFAIR, HC4 has stronger correction using diag_hat_matrix, but still computes the hat_matrix in a non-robust way (i.e. similar to nonrobust standard Mahalanobis distance).