Comparisons of Estimators of Small Proportion under Group Testing

Authors

Xing WeiFollow

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

First Advisor's Name

Jie Mi

First Advisor's Committee Title

Committee chair

Second Advisor's Name

Kai Huang

Second Advisor's Committee Title

Committee Co-Chair

Third Advisor's Name

Florence George

Third Advisor's Committee Title

committee member

Keywords

Group Testing, MLE, Burrows' Estimator, Bayes Estimator, Relative Bias, Relative Efficiency

Date of Defense

7-2-2015

Abstract

Binomial group testing has been long recognized as an efficient method of estimating proportion of subjects with a specific characteristic. The method is superior to the classic maximum likelihood estimator (MLE), particularly when the proportion is small. Under the group testing model, we assume the testing is conducted without error. In the present research, a new Bayes estimator will be proposed that utilizes an additional piece of information, the proportion to be estimated is small and within a given range. It is observed that with the appropriate choice of the hyper-parameter our new Bayes estimator has smaller mean squared error (MSE) than the classic MLE, Burrows estimator, and the existing Bayes estimator. Furthermore, on the basis of heavy Monte Carlo simulation we have determined the best hyper-parameters in the sense that the corresponding new Bayes estimator has the smallest MSE. A table of these best hyper-parameters is made for proportions within the considered range.

Identifier

FIDC000104

Recommended Citation

Wei, Xing, "Comparisons of Estimators of Small Proportion under Group Testing" (2015). FIU Electronic Theses and Dissertations. 2195.
https://digitalcommons.fiu.edu/etd/2195