I was reading Chapter 22 of Hansen's Econometrics on M-estimators and he lists OLS, Non-linear LS and Maximum Likelihood as examples of M estimators. After a few paragraphs, he also writes "[...] not all non-linear estimators are m-estimators. Examples include method of moments, GMM, and minimum distance"
My questions are:
- What does he mean when he says non-linear estimators?
- What is the difference between M-estimators and minimum distance estimators? Is OLS both an m-estimator and a minimum distance? If so, then why is GMM not considered an m-estimator?