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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?

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    $\begingroup$ This is an excellent question. I have seen many papers in statistics journals bragging about their method having an oracle property, and the paper didn't even try performance of their method on the kinds of sample sizes I see. $\endgroup$ Commented Jan 30, 2022 at 13:19

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