{"id":{"repo_id":"umkc","oai_identifier":"oai:mospace.umsystem.edu:10355/70891"},"canonical_url":"https://search.dev.ndltd.org/etd/umkc/oai:mospace.umsystem.edu:10355/70891","repository":{"repo_id":"umkc","name":"University of Missouri - Kansas City","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"Efficient sequential designs with asymptotic second-order lower bound of Bayes risk for estimating product of means","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Xia, Xing"],"institution":"University of Missouri--Kansas City","degree_name":"Ph.D. (Doctor of Philosophy)","degree_level":"Ph.D.","degree_discipline":"Mathematics (UMKC)","degree_department":null,"school":null,"contributors":[],"advisors":["Rekab, Kamel","Medhi, Deepankar"],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019","date_published":"2019","updated_at":"2026-07-24T05:18:49Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10355/70891","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Rekab, Kamel","Medhi, Deepankar"]},{"key":"dc:creator","label":"Author","values":["Xia, Xing"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-01-02T20:01:37Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-01-02T20:01:37Z"]},{"key":"dc:date.issued","label":"Date","values":["2019"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics (UMKC)","Telecommunications and Computer Networking (UMKC)"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Ph.D.","Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D. (Doctor of Philosophy)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri--Kansas City"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10355/70891"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Title from PDF of title page viewed January 8, 2020","Dissertation advisor: Kamel Rekab and Deep Medhi,","Vita","Includes bibliographical references (page 60-62)","Thesis (Ph.D.)--Department of Mathematics and Statistics, School of Computing and Engineering. University of Missouri--Kansas City, 2019"]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Efficient sequential designs with asymptotic second-order lower bound of Bayes risk for estimating product of means"]}]}],"canonical_facts":{"dc:contributor.advisor":["Rekab, Kamel","Medhi, Deepankar"],"dc:creator":["Xia, Xing"],"dc:date.accessioned":["2020-01-02T20:01:37Z"],"dc:date.available":["2020-01-02T20:01:37Z"],"dc:date.issued":["2019"],"dc:description":["Title from PDF of title page viewed January 8, 2020","Dissertation advisor: Kamel Rekab and Deep Medhi,","Vita","Includes bibliographical references (page 60-62)","Thesis (Ph.D.)--Department of Mathematics and Statistics, School of Computing and Engineering. University of Missouri--Kansas City, 2019"],"dc:description.abstract":["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."],"dc:identifier.uri":["https://hdl.handle.net/10355/70891"],"dc:title":["Efficient sequential designs with asymptotic second-order lower bound of Bayes risk for estimating product of means"],"thesis:degree_discipline":["Mathematics (UMKC)","Telecommunications and Computer Networking (UMKC)"],"thesis:degree_level":["Ph.D.","Doctoral"],"thesis:degree_name":["Ph.D. (Doctor of Philosophy)"],"thesis:institution_name":["University of Missouri--Kansas City"]},"updated_at":"2026-07-24T05:18:49Z"}