# OLS - why is it necessary to involve likelihood theory into it?

I'm trying to understand the OLS model and the assumptions behind it. I'm struggling between 2 texts with a different approach:

• nyu do not talk about likelihood estimation theory at all. They develop the Gauss-Markov theorem with a minimum amount of assumptions, and there's no reasoning to why OLS is a reasonable criteria
• princeton rely on maximum likelihood estimation from the first minute, and assume normal disturbances, which is a nice reasoning for OLS, but involve a much larger set of assumptions (I think)

What is a better approach? How do you reconcile the 2? related to OLS vs. maximum likelihood under Normal distribution in linear regression

• OLS is not a model, it is an estimator. MLE is also an estimator. The model underlying it, the linear regression model can be motivated using different principles. Gauss-Markov (geometric) and likelihood theory are ways to characterize the properties of these estimators within specific frameworks that coincide in certain cases, such as the MLE and the OLSE for the linear regression model. Oct 22, 2016 at 6:42
• If you want to do small sample statistical inference, Gauss Markov doesn't really help you. Even with large samples, if you want prediction intervals, Gauss-Markov doesn't help you make the prediction interval. Oct 22, 2016 at 11:10