The bootstrap procedure is widely used in nonparametric statistics to generate an empirical sampling distribution from a given sample data set for a statistic of interest. Generally, the results are good for location parameters such as population mean, median, and even for estimating a population correlation. However, the results for a population variance, which is a spread parameter, are not as good due to the resampling nature of the bootstrap method. Bootstrap samples are constructed using sampling with replacement; consequently, groups of observations with zero variance manifest in these samples. As a result, a bootstrap variance estimator will carry a bias to the low side. This work will attempt to demonstrate the bias issue with simulations, as well as explore possible approaches to correct for any such bias. In addition, these approaches will be evaluated for more general performance through simulations.
","abstract_html":"<p>The bootstrap procedure is widely used in nonparametric statistics to generate an empirical sampling distribution from a given sample data set for a statistic of interest. Generally, the results are good for location parameters such as population mean, median, and even for estimating a population correlation. However, the results for a population variance, which is a spread parameter, are not as good due to the resampling nature of the bootstrap method. Bootstrap samples are constructed using sampling with replacement; consequently, groups of observations with zero variance manifest in these samples. As a result, a bootstrap variance estimator will carry a bias to the low side. This work will attempt to demonstrate the bias issue with simulations, as well as explore possible approaches to correct for any such bias. In addition, these approaches will be evaluated for more general performance through simulations. </p>","abstract_has_math":false,"creators":["Nguyen, Nghia Trong"],"institution":null,"degree_name":"Master of Science - Mathematical Sciences","degree_level":"Thesis","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":["Robert Henderson","Gregory Miller","Jacob Turner"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-05-01T07:00:00Z","date_published":"2018-05-01T07:00:00Z","updated_at":"2026-07-24T04:30:15Z","subjects":["Bootstrap","Variance","Estimate","Bias","Low","Repeat","Resample","Zero","Variation","Nonparametric","Applied Statistics","Other Statistics and Probability","Probability","Statistical Methodology","Statistical Theory"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.sfasu.edu/etds/157","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Robert Henderson","Gregory Miller","Jacob Turner"]},{"key":"dc:creator","label":"Author","values":["Nguyen, Nghia Trong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-05-09T07:00:00Z"]},{"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":["Bootstrap","Variance","Estimate","Bias","Low","Repeat","Resample","Zero","Variation","Nonparametric","Applied Statistics","Other Statistics and Probability","Probability","Statistical Methodology","Statistical Theory"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.sfasu.edu/etds/157"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The bootstrap procedure is widely used in nonparametric statistics to generate an empirical sampling distribution from a given sample data set for a statistic of interest. Generally, the results are good for location parameters such as population mean, median, and even for estimating a population correlation. However, the results for a population variance, which is a spread parameter, are not as good due to the resampling nature of the bootstrap method. Bootstrap samples are constructed using sampling with replacement; consequently, groups of observations with zero variance manifest in these samples. As a result, a bootstrap variance estimator will carry a bias to the low side. This work will attempt to demonstrate the bias issue with simulations, as well as explore possible approaches to correct for any such bias. In addition, these approaches will be evaluated for more general performance through simulations.
"]},{"key":"dc:title","label":"Title","values":["Evaluation of Using the Bootstrap Procedure to Estimate the Population Variance"]}]}],"canonical_facts":{"dc:contributor":["Robert Henderson","Gregory Miller","Jacob Turner"],"dc:creator":["Nguyen, Nghia Trong"],"dc:date.available":["2018-05-09T07:00:00Z"],"dc:description.abstract":["The bootstrap procedure is widely used in nonparametric statistics to generate an empirical sampling distribution from a given sample data set for a statistic of interest. Generally, the results are good for location parameters such as population mean, median, and even for estimating a population correlation. However, the results for a population variance, which is a spread parameter, are not as good due to the resampling nature of the bootstrap method. Bootstrap samples are constructed using sampling with replacement; consequently, groups of observations with zero variance manifest in these samples. As a result, a bootstrap variance estimator will carry a bias to the low side. This work will attempt to demonstrate the bias issue with simulations, as well as explore possible approaches to correct for any such bias. In addition, these approaches will be evaluated for more general performance through simulations.
"],"dc:identifier":["https://scholarworks.sfasu.edu/etds/157"],"dc:subject":["Bootstrap","Variance","Estimate","Bias","Low","Repeat","Resample","Zero","Variation","Nonparametric","Applied Statistics","Other Statistics and Probability","Probability","Statistical Methodology","Statistical Theory"],"dc:title":["Evaluation of Using the Bootstrap Procedure to Estimate the Population Variance"],"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"}