This thesis is based on a Poisson model that uses both error-free data and error-prone data subject to misclassification in the form of false-negative and false-positive counts. We present maximum likelihood estimators (MLEs), Fisher's Information, and Wald statistics for Poisson rate parameter and the two misclassification parameters. Next, we invert the Wald statistics to get asymptotic confidence intervals for Poisson rate parameter and false-negative rate parameter. The coverage and width properties for various sample size and parameter configurations are studied via a simulation study. Finally, we apply the MLEs and confidence intervals to one real data set and another realistic data set.
","abstract_html":"<p>This thesis is based on a Poisson model that uses both error-free data and error-prone data subject to misclassification in the form of false-negative and false-positive counts. We present maximum likelihood estimators (MLEs), Fisher's Information, and Wald statistics for Poisson rate parameter and the two misclassification parameters. Next, we invert the Wald statistics to get asymptotic confidence intervals for Poisson rate parameter and false-negative rate parameter. The coverage and width properties for various sample size and parameter configurations are studied via a simulation study. Finally, we apply the MLEs and confidence intervals to one real data set and another realistic data set.</p>","abstract_has_math":false,"creators":["Poddiwala Hewage, Nishantha Janith Chandrasena"],"institution":null,"degree_name":"Master of Science - Mathematical Sciences","degree_level":"Thesis","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":["Kent Riggs","Robert K. Henderson","Jacob Turner"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-08-01T07:00:00Z","date_published":"2018-08-01T07:00:00Z","updated_at":"2026-07-24T04:30:15Z","subjects":["Wald Statistics","Fisher's Information","Poisson Parameter","Asymptotic Confidence Intervals","Misclassification Parameter","Maximum Likelihood Estimators","Mathematics","Physical Sciences and Mathematics","Statistical Models","Statistical Theory","Statistics and Probability"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.sfasu.edu/etds/202","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kent Riggs","Robert K. Henderson","Jacob Turner"]},{"key":"dc:creator","label":"Author","values":["Poddiwala Hewage, Nishantha Janith Chandrasena"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-08-09T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science - Mathematical Sciences"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Wald Statistics","Fisher's Information","Poisson Parameter","Asymptotic Confidence Intervals","Misclassification Parameter","Maximum Likelihood Estimators","Mathematics","Physical Sciences and Mathematics","Statistical Models","Statistical Theory","Statistics and Probability"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.sfasu.edu/etds/202"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis is based on a Poisson model that uses both error-free data and error-prone data subject to misclassification in the form of false-negative and false-positive counts. We present maximum likelihood estimators (MLEs), Fisher's Information, and Wald statistics for Poisson rate parameter and the two misclassification parameters. Next, we invert the Wald statistics to get asymptotic confidence intervals for Poisson rate parameter and false-negative rate parameter. The coverage and width properties for various sample size and parameter configurations are studied via a simulation study. Finally, we apply the MLEs and confidence intervals to one real data set and another realistic data set.
"]},{"key":"dc:title","label":"Title","values":["Wald Confidence Intervals for a Single Poisson Parameter and Binomial Misclassification Parameter When the Data is Subject to Misclassification"]}]}],"canonical_facts":{"dc:contributor":["Kent Riggs","Robert K. Henderson","Jacob Turner"],"dc:creator":["Poddiwala Hewage, Nishantha Janith Chandrasena"],"dc:date.available":["2018-08-09T07:00:00Z"],"dc:description.abstract":["This thesis is based on a Poisson model that uses both error-free data and error-prone data subject to misclassification in the form of false-negative and false-positive counts. We present maximum likelihood estimators (MLEs), Fisher's Information, and Wald statistics for Poisson rate parameter and the two misclassification parameters. Next, we invert the Wald statistics to get asymptotic confidence intervals for Poisson rate parameter and false-negative rate parameter. The coverage and width properties for various sample size and parameter configurations are studied via a simulation study. Finally, we apply the MLEs and confidence intervals to one real data set and another realistic data set.
"],"dc:identifier":["https://scholarworks.sfasu.edu/etds/202"],"dc:subject":["Wald Statistics","Fisher's Information","Poisson Parameter","Asymptotic Confidence Intervals","Misclassification Parameter","Maximum Likelihood Estimators","Mathematics","Physical Sciences and Mathematics","Statistical Models","Statistical Theory","Statistics and Probability"],"dc:title":["Wald Confidence Intervals for a Single Poisson Parameter and Binomial Misclassification Parameter When the Data is Subject to Misclassification"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science - Mathematical Sciences"]},"updated_at":"2026-07-24T04:30:15Z"}