Performance of Bootstrap Confidence Region For Binomial Distribution With Unknown Parameters p and m

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.

Name thesis:degree_name

Master of Science (MSc)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Statistics

Grantor dc:publisher

Faculty of Graduate Studies and Research, University of Regina

Year dc:date.issued

2020

Author dc:creator

• Gao, Chengu

Advisor dc:contributor.advisor

• Volodin, Andrei

Committee member dc:contributor.committeemember

• Deng, DianLiang

Language dc:language.iso

en

DOI

https://doi.org/10.82465/3858

OAI identifier oai:identifier

oai:uregina.scholaris.ca:10294/9341