In the paper “TWEEDIE’S FORMULA AND SELECTION BIAS” the author Bradley Efron said the MLE can cause selection bias, which confuses me a lot.

We suppose that the statistician observes some large number of estimates $z_i$, each with its own unobserved expectation parameter $\mu_i$. The largest few of the $z_i$'s are likely to substantially overestimate their corresponding $\mu_i$'s, this being an example of selection bias, or regression to the mean."

Could anyone tell me why the MLE can cause selection bias when select subset of variables from large-scale predictors?


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