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The material in section 6 deals with this result, and the large related literature that has followed. In many problems, as in the previous paragraph, Bayes or Generalized Bayes estimators are known to form a complete class. When loss is quadratic and the prior (and hence typically the posterior) distribution is not degenerate at a point, the Bayes estimator cannot take values on the boundary of the parameter space. There are many results in the literature that use this phenomenon to determine inadmissibility of certain estimators that take values on (or near) the boundary.

Estimation with quadratic loss. In Proc. Fourth Berkeley Symp. Math. Statist. Probab. 1, 361–380. Berkeley: University of California Press. MR133191 [15] Johnson, B. (1991). On the admissibility of improper Bayes inferences in fair Bayes decision problems. D. Thesis, University of Minnesota. [16] Johnstone, I. (1984). Admissibility, difference equations and recurrence in estimating a Poisson mean. Ann. Statist. 12, 1173–1198. MR760682 [17] Johnstone, I. (1986). Admissible estimation, Dirichlet principles, and recurp .

1993). Markov Chains and Stochastic Stability. New York: Springer-Verlag. MR1287609 [22] Revuz, D. (1984). Markov Chains, 2nd Edition. North Holland, Amsterdam. MR415773 [23] Smith, J. Q. (1994). The inadmissibility of certain Bayes decision rules under vague priors in location problems. J. R. S. S. - B. 56, 543–548. MR1278226 [24] Srinivasan, C. (1981). Admissible generalized Bayes estimators and exterior boundary value problems. Sankhya Ser. A. 43, 1–25. MR656265 [25] Stein, C. (1955). A necessary and sufficient condition for admissibility.

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