The philosophical significance of Stein’s paradox
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Charles Stein discovered a paradox in 1955 that many statisticians think is of fundamental importance. Here we explore its philosophical implications. We outline the nature of Stein’s result and of subsequent work on shrinkage estimators; then we describe how these results are related to Bayesianism and to model selection criteria like AIC. We also discuss their bearing on scientific realism and instrumentalism. We argue that results concerning shrinkage estimators underwrite a surprising form of holistic pragmatism.
KeywordsStein’s paradox Shrinkage estimators Bayesianism Frequentism Statistical decision theory
We thank Marty Barrett, Larry Brown, Jan.-Willem Romeijn, Teddy Seidenfeld, Mike Steel, Reuben Stern, and the anonymous referees for very useful comments. This paper is dedicated to the memory of Charles Stein (1920-2016).
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No funding to declare.
Conflict of interest
We declare we have no conflicts of interest.
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