Can all three criteria ML, MMSE, and LS be called regressor, estimator, and predictor ?
If not, an intuitive explanation of why they can't be would be good.
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All of them are estimators in a model (PDF of Parameters in the ML, Numeric Model in the LS or Bayesian Model for the MMSE).
Predictor is a term for predicting future data based on given data. Any of the method above can do that with different assumption of the model.
Regressor is a term for predicting model parameters from a given data. Again any of the above can be used to do so.
So you need to separate the means you use (Type of estimator and model) for the object you try to achieve (Predict, Regress, Smooth, etc...).