An interval estimation procedure with deterministic stopping rule in Bayes sequential interval estimation

The problem of Bayes sequential interval estimation of the mean of a normal distribution with known variance is considered. An interval estimation procedure, which does not depend on the prior distribution, with deterministic stopping rule is proposed in this paper. It is shown that the proposed procedure is asymptotically pointwise optimal and asymptotically Bayes in the sense of Bickel and Yahav (Proceedings of the Fifth Berkeley Symposium on Mathematics and Statistical Probability, Vol. 1, University of California Press, California, 1967, pp. 401-413; Ann. Math. Statist. 39 (1968) 442-456.) for a large class of prior distributions.