The problem of Bayes sequent.ial int.erval estimation was discussed in many papers, for example: Blumenthal(1970) and Gieser and Knute (1976). Based on those papers, we know that the interval estimation procedures always depend on t.he prior distribution. This paper will consider t.he problem of the Bayes sequential int.erval estimation of t.he mean of a normal distribution with known variance. We propose an interval estimation procedure with deterministic stopping rule. The proposed interval estimation procedure does not depend on the prior and it is shown to be asymptotically point optimal (A.P.O.) and asymptotically Bayes in the sense of Bickel and Yahav (1967, 1968) for a large class of prior distributions.
2000年國際數學與統計研討會暨第34屆中華民國數學會年會：慶祝淡江大學創校五十週年校慶 (2000 international conference on mathematics and statistics and 34th annual meeting of mathematical society of R.O.C. : commemorating the 50th anniversary of Tamkang University), pp.89