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Charles M. Stein changed the theory of estimation by showing that estimating several normal means together can permit improvement over their separate usual estimates under a combined squared-error loss. The James–Stein estimator expresses this phenomenon through shrinkage: introducing bias can lower the total mean squared error when variance is reduced sufficiently. The guarantee concerns the specified aggregate loss, rather than promising a better estimate for every coordinate in every dataset.

Stein also developed tools connecting normal distributions, derivatives and probability approximations. With Bradley Efron, he coauthored The Jackknife Estimate of Variance by Bradley Efron and Charles M. Stein, a source associated with the Efron–Stein inequality. His Stanford obituary records his mathematical career and death in 2016.^[ref]