Seth Axen 🪓 May 17, 2023
Does anyone know of an algorithm for the weighted median that supports negative weights? #statistics
Show threadMarkus JänttiMay 17, 2023
@sethaxen I'm curious - what is the interpretation of a negative weight for an observation?
Show threadSeth Axen 🪓 May 17, 2023

@mjantti No interpretation necessary. The goal is to find a global minimizer of the weighted sum of distances from the data. With negative weights, the function may no longer be convex, so I don't expect such an algorithm exists, but it would be nice if it does.

One place this comes up is in computing the weighted median of data on the circle. One can reframe the problem as one of computing the usual linear median but where some weights are negative.

Show threadIan HolmesMay 17, 2023
@mjantti @sethaxen so it’s like it’s maximizing distance to some (negatively-weighted) points, while minimizing distance to other (positively-weighted) ones?
Show threadSeth Axen 🪓 
@ianholmes @mjantti Yes, that's right.
May 17, 2023 at 4:10pmWeb
Show threadMarkus JänttiMay 17, 2023
@sethaxen @ianholmes You've probably checked all standard sources so recommending the references in R's package quantreg is unlikely to help you. Interesting and to me entirely new problem!