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

Having worked on Empirical Bayes credibility for a combined total of over ten years, we share Mr. Buck’s frustration at the slow acceptance in practice of Empirical Bayes techniques. Part of the reason, we believe, is the inherent conservatism of the insurance business. Considering the sums at stake, practicing actuaries are reluctant to adopt new methods until they have been thoroughly researched and tested. It is gladdening, then, to see further discussion of credibility in the Proceedings. Only after undergoing thorough scrutiny can new methods hope to be adopted in practice. Mr. Buck has written a paper that considers one aspect of credibility-stein estimation-from a theoretical point of view. Lay actuaries hoping to see a comparison based on real data of an Empirical Bayes credibility procedure and (say) the square root rule must look elsewhere. But Mr. Buck’s paper could still have relevance to lay actuaries. If a method can be shown to be theoretically incorrect, there is no reason to test it on real data.