Stein’s paradox in statistics is a surprising result that challenges the idea of making guesses about means in Gaussian distributions. While in one or two dimensions, guessing the mean as the sample is reasonable, in three dimensions or more, the James-Stein estimator provides a better guess. This estimator scales the sample towards the origin, correcting for the tendency of high-dimensional samples to be further from the mean. This correction reduces the overall risk of the estimate, showcasing the bias-variance tradeoff. Strangely, the choice of origin contains information about the mean, debunking the idea of arbitrariness in coordinate systems. The James-Stein estimator’s effectiveness is due to clever geometric techniques that maximize the accuracy of guesses in high-dimensional spaces.
https://joe-antognini.github.io/machine-learning/steins-paradox