[Feature] Weighted Least Squares algorithm #110
Description
Feature description
We are writing a recommendations paper recommending WLS fitting. Currently, Ben implemented a WLS based on the recommendations paper, but did this from scratch (no dedicated tools). I would be curious as to how "reproducible" our recommendations are (i.e. people who read the paper and implement the algorithm may still end up with different solutions). This would be very valuable information and would strongly point to the need for an open source repository (us!)
If you want to work on this, pop me (oliverchampion) a message and I can send you the wording in the recommendations paper.
Describe the solution
A WLS in accoordance with the recommendations paper.
We could add a WLS recommendations approach based on this paper https://www.sciencedirect.com/science/article/pii/S1053811913005223 but using the build in WLS from statsmodel:
Comment from Eric:
If the iterative route is the way, here's the documentation for the weighting functions you can choose in RLM: https://www.statsmodels.org/dev/rlm.html#norms
And here are the plots of those functions: https://www.statsmodels.org/dev/rlm_techn1.html
The stopping and iteration is here: https://www.statsmodels.org/stable/generated/statsmodels.robust.robust_linear_model.RLM.fit.html#statsmodels.robust.robust_linear_model.RLM.fit
I think the re-weighting is also there, in the scale_est parameter. I think the mad option there might be somewhat similar to what you're using?
It's definitely more complicated but it might be worth exploring as it has some more options and comes pre-tested.
Describe alternatives
Anyone with alternative ways to implement the approach, please do! The more the merrier for our point.
E.g. in Matlab?
Additional context
No response
Are you working on this?
None