This phenomenon is closely related to “regression towards the mean”. It is important, when discussing something like this, to include such jargon names, because there is a lot of existing writing and thought on the topic. Don’t reinvent the wheel.
I think they’re close to identical. “The tails come apart”, “regression to the mean”, “regressional Goodhart”, “the winner’s curse”, “the optimizer’s curse”, and “the unilateralist’s curse” are all talking about essentially the same statistical phenomenon. They come at it from different angles, and highlight different implications, and are evocative of different contexts where it is relevant to account for the phenomenon.
The expectation of X is “regressed towards the mean” when an extreme Y is used as a predictor, and vice versa. Thus, to my mind, this post’s target phenomenon is a straightforward special case of RTM.
Hmm, okay yeah that makes sense. I think my initial confusion is something like “the most interesting takeaway here is not the part where predictor regressed to the mean, but that extreme things tend to be differently extreme on different axis.
(At least, when I refer mentally to “tails coming apart”, that’s the thing I tend to mean)
the most interesting takeaway here is not the part where predictor regressed to the mean, but that extreme things tend to be differently extreme on different axis.
Even though the two variables are strongly correlated, things that are extreme on one variable are somewhat closer to the mean on the other variable.
This phenomenon is closely related to “regression towards the mean”. It is important, when discussing something like this, to include such jargon names, because there is a lot of existing writing and thought on the topic. Don’t reinvent the wheel.
Other than that, it’s a fine article.
How related is this to regression to the mean? It seems like a quite different phenomenon at first glance to me.
I think they’re close to identical. “The tails come apart”, “regression to the mean”, “regressional Goodhart”, “the winner’s curse”, “the optimizer’s curse”, and “the unilateralist’s curse” are all talking about essentially the same statistical phenomenon. They come at it from different angles, and highlight different implications, and are evocative of different contexts where it is relevant to account for the phenomenon.
The expectation of X is “regressed towards the mean” when an extreme Y is used as a predictor, and vice versa. Thus, to my mind, this post’s target phenomenon is a straightforward special case of RTM.
Hmm, okay yeah that makes sense. I think my initial confusion is something like “the most interesting takeaway here is not the part where predictor regressed to the mean, but that extreme things tend to be differently extreme on different axis.
(At least, when I refer mentally to “tails coming apart”, that’s the thing I tend to mean)
Even though the two variables are strongly correlated, things that are extreme on one variable are somewhat closer to the mean on the other variable.
Gotcha. Yeah that makes sense.