Efficient sequential designs with asymptotic second-order lower bound of Bayes risk for estimating product of means

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.

Name thesis:degree_name

Ph.D. (Doctor of Philosophy)

Level thesis:degree_level

Ph.D.

Discipline thesis:degree_discipline

Mathematics (UMKC)

Grantor

University of Missouri--Kansas City

Year dc:date.issued

2019

Author dc:creator

• Xia, Xing

Advisors dc:contributor.advisor

• Rekab, Kamel
• Medhi, Deepankar

Handle dc:identifier.uri

https://hdl.handle.net/10355/70891

OAI identifier oai:identifier

oai:mospace.umsystem.edu:10355/70891