Bounds and Asymptotic Expansions for Solutions of the Free Boundary Problems Related to Sequential Decision Versions of a Bioequivalence Problem
HARVARD UNIV CAMBRIDGE MA DEPT OF STATISTICS
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The numerical solutions of two related variations of a sequential version of a form 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 It that report he referred to our unpublished results bounding the solutions and providing asymptotic expansions.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 to 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 Hwangs 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,ss0 into a continuation set C and a stopping set S.
- Statistics and Probability