Bounds and Asymptotic Expansions for Solutions of the Free Boundary ProblemsRelated to Sequential Decision Versions of a Bioequivalence Problem

摘要

The numerical solutions of two related variations of a sequential version of aform of the bioequivalence problem was presented in a report by Hwang (1991). It that report he referred to our unpublished results bounding the solutions and providing asymptotic expansions. The present report has two major functions. One is to derive and amplify these results, and incidentally to correct error. The second is to gather together in one place, and with relatively little of the abbreviation characteristics of previous publications, many of the details that are useful in deriving the asymptotic expansions, e.g., see Breakwell and Chernoff (1964), Chernoff (1964a, 1972), and Chernoff and Petkau (1981). In Hwang's report he presented the Bayesian decision theoretic approach in which the problem is related to a stopping problem involving Brownian motion, a stopping cost represented by a single cost parameter c, and an initial point (y,s) depending on the prior normal distribution of an unknown parameter and other known parameters of the problem. The solution of the problem is represented by dividing up the set (y,s):s>0 into a continuation set C and a stopping set S.