Efficient sequential designs with asymptotic second-order lower bound of Bayes risk for estimating product of means
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In order to estimate the reliability of sequentially designed procedures under the Bayesian framework with conjugate priors, a sharp lower bound for the Bayes risk has been derived. Chapter 1 and 2 introduce the background and fundamental concepts and theorems of this study. Chapter 3 focuses on deriving second-order efficiency of Bayes risk for two independent components in the one-parameter exponential family which includes the most common distribution in application of reliability testing, Bernoulli distribution. Chapter 3 also uses Monte Carlo simulations with several proposed sequential designs to illustrate optimality of the second-order efficiency. Then Chapter 4 extends the result to k (k>2) independent components sequentially designed systems. The same Monte Carlo simulations were performed to assure that the second order lower bound is achieved.
Table of Contents
Introduction -- Conceptual framework -- Second-order efficiency for estimating product of 2 components in exponential family -- Second-order efficiency for estimating product of K components -- Conclusion
Ph.D. (Doctor of Philosophy)