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I am aware that a question very similar to mine has already been asked here (Should AIC be reported on training or test data?), but some points remain unclear to me.

The accepted answer states:

On the other hand, when the model is evaluated on test data (not the same as the training data), there is no bias to −2ln(L) . Therefore, it does not make sense to penalize it by 2p , so using AIC does not make sense; you can use −2ln(L) directly.

Could someone elaborate more on this? I don't see why the number of parameters in a model is relevant in the train data, but not anymore in the test data.

Is it correct that the AIC is only a measure for in-sample performance then?

eork
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  • Suppose that you have two models one with $p$ parameters and another one with $p+1$ parameters and you fit them on the training data set you would use the AIC to compare them right? Now, let's say that someone else comes two you with two different models that have been already fitted. You don't care about how these models were evaluated. Based on that you would like to know which one maximizes the most the likelihood function. – Fiodor1234 Jun 01 '23 at 21:42

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