# Is maximum likelihood estimation meaningless for a dataset of only outliers?

From my understanding, maximum likelihood estimation chooses the set of parameters for the estimator that maximizes likelihood with the ground truth distribution.

I always interpreted it as the training set having a tendency to have most examples near the mean or the expected value of the true distribution. Since most training examples are close to the mean (since they have been sampled from this distribution) maximizing the estimator's chance of sampling these examples gets the estimated distribution close to the ground truth distribution.

This would mean that any MLE procedure on a dataset of outliers should fail miserably. Are this interpretation and conclusion correct? If not, what is wrong with the mentioned interpretation of maximizing likelihood for an estimator?

• Yes it's correct. Also it's not only in the case of MLE. Any classifier trying to maximize it's performance w.r.t sampled data has some chance of failure. – DuttaA Apr 4 at 6:22