= Charles M. Stein
{c}
{title2=1920–2016}
{wiki}
= Charles Stein
{c}
{synonym}
= C. Stein
{c}
{synonym}
<Charles M. Stein> changed the theory of estimation by showing that estimating several normal <mean>[means] together can permit improvement over their separate usual estimates under a combined <squared-error loss>[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 function>[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.https://news.stanford.edu/stories/2016/12/charles-m-stein-extraordinary-statistician-anti-war-activist-dies-96[Stanford institutional obituary, 1 December 2016]{ref}
https://news.stanford.edu/stories/2016/12/charles-m-stein-extraordinary-statistician-anti-war-activist-dies-96
\Image[https://project-orion-production.s3.amazonaws.com/uploads/content/295/IMG.jpeg]
{title=Portrait of Charles M. Stein}
{width=220}
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