{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/9341"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/9341","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Performance of Bootstrap Confidence Region For Binomial Distribution With Unknown Parameters p and m","abstract":"The goal of this research is to find out the Performance of the bootstrap confidence region of a binomial distribution with unknown parameters. The research is designed as follow: The first step is to estimate unknown parameters m and p from binomial distribution. In my case, I focus on method of moment to estimate. Since these estimators do not have moments of all orders, I cannot obtain the mean, variance, and covariance for these estimators. Thus, the Delta Method is used to derive the asymptotic normality of the joint distribution of the Method of Moments estimators. After finding the estimators pˆ, and mˆ , I will work on the Asymptotic Normality of the Estimators. For Asymptotic Normality of the Estimators by method of moment, I will find the sampling from the binomial distribution with sample mean X¯ − mp and sample variance S2 − mp(1 − p) are asymptotically normal with zero mean vector and covariance matrix. I will apply the Delta-method consists of expansion of pˆ, and mˆ into two-dimensional Taylor series expansion, then using partial derivatives of these functions, so I should have the covariance matrix. Next section, I find out that if random vector X is normally distributed with the mean vector E and covariance matrix Σ is distributed as chi-square with 2 degrees of freedom. Therefore, the 100(1 − α)% confidence region should be X2(p, m) ≤ X2(α) with 2 degree of freedom. Some general steps of using the independent and dependent bootstrap sampling will be the next. I will give example of creating both independent and dependent bootstrap samples with different k, where k is the number of copies of original sample. I also will talk about the coverage probability of confidence regions and the areas of confidence regions.","abstract_html":"The goal of this research is to find out the Performance of the bootstrap confidence region of a binomial distribution with unknown parameters. The research is designed as follow: The first step is to estimate unknown parameters m and p from binomial distribution. In my case, I focus on method of moment to estimate. Since these estimators do not have moments of all orders, I cannot obtain the mean, variance, and covariance for these estimators. Thus, the Delta Method is used to derive the asymptotic normality of the joint distribution of the Method of Moments estimators. After finding the estimators pˆ, and mˆ , I will work on the Asymptotic Normality of the Estimators. For Asymptotic Normality of the Estimators by method of moment, I will find the sampling from the binomial distribution with sample mean X¯ − mp and sample variance S2 − mp(1 − p) are asymptotically normal with zero mean vector and covariance matrix. I will apply the Delta-method consists of expansion of pˆ, and mˆ into two-dimensional Taylor series expansion, then using partial derivatives of these functions, so I should have the covariance matrix. Next section, I find out that if random vector X is normally distributed with the mean vector E and covariance matrix Σ is distributed as chi-square with 2 degrees of freedom. Therefore, the 100(1 − α)% confidence region should be X2(p, m) ≤ X2(α) with 2 degree of freedom. Some general steps of using the independent and dependent bootstrap sampling will be the next. I will give example of creating both independent and dependent bootstrap samples with different k, where k is the number of copies of original sample. I also will talk about the coverage probability of confidence regions and the areas of confidence regions.","abstract_has_math":false,"creators":["Gao, Chengu"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Master of Science (MSc)","degree_level":"Master's","degree_discipline":"Statistics","degree_department":null,"school":null,"contributors":[],"advisors":["Volodin, Andrei"],"committee_chairs":[],"committee_members":["Deng, DianLiang"],"year":2020,"date_issued":"2020-04","date_published":"2020-04","updated_at":"2026-07-24T04:03:27Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/3858"],"render_values":[{"text":"https://doi.org/10.82465/3858","href":"https://doi.org/10.82465/3858","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/9341","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Volodin, Andrei"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Deng, DianLiang"]},{"key":"dc:creator","label":"Author","values":["Gao, Chengu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-12-13T16:31:50Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-12-13T16:31:50Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-04"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MSc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/3858"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/9341"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. x, 100 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["The goal of this research is to find out the Performance of the bootstrap confidence region of a binomial distribution with unknown parameters. The research is designed as follow: The first step is to estimate unknown parameters m and p from binomial distribution. In my case, I focus on method of moment to estimate. Since these estimators do not have moments of all orders, I cannot obtain the mean, variance, and covariance for these estimators. Thus, the Delta Method is used to derive the asymptotic normality of the joint distribution of the Method of Moments estimators. After finding the estimators pˆ, and mˆ , I will work on the Asymptotic Normality of the Estimators. For Asymptotic Normality of the Estimators by method of moment, I will find the sampling from the binomial distribution with sample mean X¯ − mp and sample variance S2 − mp(1 − p) are asymptotically normal with zero mean vector and covariance matrix. I will apply the Delta-method consists of expansion of pˆ, and mˆ into two-dimensional Taylor series expansion, then using partial derivatives of these functions, so I should have the covariance matrix. Next section, I find out that if random vector X is normally distributed with the mean vector E and covariance matrix Σ is distributed as chi-square with 2 degrees of freedom. Therefore, the 100(1 − α)% confidence region should be X2(p, m) ≤ X2(α) with 2 degree of freedom. Some general steps of using the independent and dependent bootstrap sampling will be the next. I will give example of creating both independent and dependent bootstrap samples with different k, where k is the number of copies of original sample. I also will talk about the coverage probability of confidence regions and the areas of confidence regions."]},{"key":"dc:title","label":"Title","values":["Performance of Bootstrap Confidence Region For Binomial Distribution With Unknown Parameters p and m"]}]}],"canonical_facts":{"dc:contributor.advisor":["Volodin, Andrei"],"dc:contributor.committeemember":["Deng, DianLiang"],"dc:creator":["Gao, Chengu"],"dc:date.accessioned":["2020-12-13T16:31:50Z"],"dc:date.available":["2020-12-13T16:31:50Z"],"dc:date.issued":["2020-04"],"dc:description":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. x, 100 p."],"dc:description.abstract":["The goal of this research is to find out the Performance of the bootstrap confidence region of a binomial distribution with unknown parameters. The research is designed as follow: The first step is to estimate unknown parameters m and p from binomial distribution. In my case, I focus on method of moment to estimate. Since these estimators do not have moments of all orders, I cannot obtain the mean, variance, and covariance for these estimators. Thus, the Delta Method is used to derive the asymptotic normality of the joint distribution of the Method of Moments estimators. After finding the estimators pˆ, and mˆ , I will work on the Asymptotic Normality of the Estimators. For Asymptotic Normality of the Estimators by method of moment, I will find the sampling from the binomial distribution with sample mean X¯ − mp and sample variance S2 − mp(1 − p) are asymptotically normal with zero mean vector and covariance matrix. I will apply the Delta-method consists of expansion of pˆ, and mˆ into two-dimensional Taylor series expansion, then using partial derivatives of these functions, so I should have the covariance matrix. Next section, I find out that if random vector X is normally distributed with the mean vector E and covariance matrix Σ is distributed as chi-square with 2 degrees of freedom. Therefore, the 100(1 − α)% confidence region should be X2(p, m) ≤ X2(α) with 2 degree of freedom. Some general steps of using the independent and dependent bootstrap sampling will be the next. I will give example of creating both independent and dependent bootstrap samples with different k, where k is the number of copies of original sample. I also will talk about the coverage probability of confidence regions and the areas of confidence regions."],"dc:identifier.doi":["https://doi.org/10.82465/3858"],"dc:identifier.uri":["https://hdl.handle.net/10294/9341"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Performance of Bootstrap Confidence Region For Binomial Distribution With Unknown Parameters p and m"],"dc:type":["master thesis"],"thesis:degree_discipline":["Statistics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:27Z"}