Evaluation of Using the Bootstrap Procedure to Estimate the Population Variance

<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>

Name thesis:degree_name

Master of Science - Mathematical Sciences

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics and Statistics

Year dc:date.available

2018

Author dc:creator

• Nguyen, Nghia Trong

Contributors dc:contributor

• Robert Henderson
• Gregory Miller
• Jacob Turner

• Bootstrap
• Variance
• Estimate
• Bias
• Low
• Repeat
• Resample
• Zero
• Variation
• Nonparametric
• Applied Statistics
• Other Statistics and Probability
• Probability
• Statistical Methodology
• Statistical Theory

Repository record dc:identifier

https://scholarworks.sfasu.edu/etds/157

OAI identifier oai:identifier

oai:scholarworks.sfasu.edu:etds-1172