On Stein Estimators: "Inadmissibility" of Admissibility as a Criterion for Selecting Estimators

Stein estimators are an alternative (non-Bayesian) explanation for credibility. Until this year, the syllabus for Part 4 of the Society’s examinations contained an article discussing Stein estimators, or James- Stein estimators, as part of the credibility readings for the exam (21. The article focuses on some examples where Stein estimators are applied to baseball players’ batting averages, among other things. In the examples, Stein estimators seem much like Bayesian credibility estimators and, in fact, credibility estimators derived from Stein’s theory have been used by the Insurance Services Office for products liability classification ratemaking. Alike as Stein estimators and Bayesian credibility estimators are in practice, the theory behind Stein estimators is very much different and does not make much sense from the author’s point of view. This paper consists of a discussion of the theory that underlies Stein estimators, including an example which illustrates the flaw in logic behind this alternative explanation of credibility.