I read this question while studying adaptive LASSO, and while I think I have a decent understanding of the oracle property in theory, I am confused about what it means to use an oracle vs. non-oracle property in every day practice.
I know that in general, an oracle procedure tends to sacrifice predictive power in order to find the "true" model. But despite being consistent in variable selection, the oracle procedure will not always generate the true model, because I don't have an infinite sample.
So, does using an oracle procedure have practical advantages over a non-oracle procedure? If using the oracle procedure doesn't guarantee correct model selection 100% of the time, what benefit do I gain from using it?