1/ #Python data science tip: To obtain a better estimate (on average) for a vector of multiple parameters, it is better to analyze sample vectors in aggregate than to use the mean of each component.
Surprisingly, this works even if the components are unrelated to one another.
Surprisingly, this works even if the components are unrelated to one another.
2/ One example comes from baseball.
Individual batting averages near the beginning of the season aren't as good of a performance predictor as individual batting averages that have been “shrunk” toward the collective mean.
Shockingly, this also works for unrelated variables.
Individual batting averages near the beginning of the season aren't as good of a performance predictor as individual batting averages that have been “shrunk” toward the collective mean.
Shockingly, this also works for unrelated variables.
3/ If this seems unintuitive, then you're not alone. That is why it is called Stein's paradox 😉
The reason it works is that errors in one estimate tend to cancel the errors in the other estimates.
statweb.stanford.edu/~ckirby/brad/o…
The reason it works is that errors in one estimate tend to cancel the errors in the other estimates.
statweb.stanford.edu/~ckirby/brad/o…
4/ The previously linked article is an easy read and explains the phenomenon in plain English and with understandable examples.
For a more terse and mathy explanation, see
en.wikipedia.org/wiki/James%E2%…
For a more terse and mathy explanation, see
en.wikipedia.org/wiki/James%E2%…
5/ "In practical terms, if the combined error is in fact of interest, then a combined estimator should be used, even if the underlying parameters are independent." -- Wikipedia article.
en.wikipedia.org/wiki/Stein%27s…
en.wikipedia.org/wiki/Stein%27s…
