Chenglu Dai

Date of Award

2008

Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

William A. Halteman

Second Committee Member

David Hiebeler

Third Committee Member

Robert Franzosa

Abstract

In many ecological research studies, abundance data, which usually contain a large number of zeros, are skewed. Therefore, it has been recently advocated that profile likelihood confidence intervals, which are generally not symmetric, be used in studies of such kind of data. Fletcher et al. (2007) shows how to numerically calculate the profile likelihood confidence intervals, using the Lagrange multiplier method. Following the authors' footprint, I not only succeed in understanding the deep wisdom by filling in the theoretical proofs, but am able to extend this method to a more complicated data set as well. On the other hand, there is actually an alternative approach to get asymmetric confidence intervals. This approach is called the bootstrap method, which is a recently developed computer-based method for assigning measures of accuracy to statistical estimates. The whole bootstrap methodology provides more than ten slightly different ways to get confidence intervals. Among all of them, I choose the bootstrap percentile method, based on which I make a direct comparison to the profile likelihood method.

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