If you’re interested, “When is Goodhart catastrophic?” characterizes some conditions on the noise and signal distributions (or rather, their tails) that are sufficient to guarantee being screwed (or in business) in the limit of many studies.
The downside is that because it doesn’t make assumptions about the distributions (other than independence), it sadly can’t say much about the non-limiting cases.
If you’re interested, “When is Goodhart catastrophic?” characterizes some conditions on the noise and signal distributions (or rather, their tails) that are sufficient to guarantee being screwed (or in business) in the limit of many studies.
The downside is that because it doesn’t make assumptions about the distributions (other than independence), it sadly can’t say much about the non-limiting cases.