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]]>Would be worth checking out although I’d need to figure out my old code.

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]]>Thank you for writing this useful article! I am curious whether you have also considered the following estimator:

Use Z_1 to build models, Z_2 to select one of them, and then reuse all of Z to (re)estimate the chosen model’s parameters.

(For instance, in your example 3.2, you might fit a full stepwise path using Z_1. Then choose a model from that path using AICs computed on Z_2. Finally refit the chosen model on all of Z.)

I imagine this could do at least as well as SAFE.

It also seems commonly used in practice. For example, it’s analogous to the usual strategy of cross-validating to choose lambda for Lasso, then refitting the full dataset at that lambda.

If you do not have time to try this yourself, would you be willing to share your code?

Best wishes,

Jerzy

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