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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?

Equations of weight functions Graphs of weight functions 2

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.

Peter Smith
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    by three functions are you talking about the influence function being one of them, or some specific class of M-estimator like GM-, R-, S-estimators that go through several steps in-between to reach a final result – develarist Jul 10 '20 at 00:24
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    Yes, score function = influence function – Peter Smith Jul 10 '20 at 08:21

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