I have spent a lot of time reading about Robust regression, especially M- estimators and their related functions (objective function, score function, and weight function). I know that M-estimators have high relative efficiency and low breakdown points.
My question is
Why each M- estimate has three functions?
Because I understand that the objective function is the one we should care about. This means when I want to develop a new robust regression, I should only think about creating a new objective function.