A reexamination of stein's antifiducial example

In Stein's 1959 example, for any sample with n sufficiently large, there is a confidence set embedded simultaneously within two regular confidence belts—one with coverage frequency smaller than an arbitrary positive ϵ, the other with coverage frequency larger than 1 — ϵ. Thus, Stein's example may be seen as an extreme case of mutually conflicting confidence statements, illustrating a possibility anticipated and denounced by Fisher.