Date of Award

5-2016

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Haiyan Su

Committee Member

Andrew McDougall

Committee Member

Andrada Ivanescu

Abstract

Empirical likelihood is a nonparametric method of statistical inference which was introduced by Owen. It allows the data analyst to use it without making distribution assumptions. Empirical likelihood method has been widely used not only for nonparametric models but also for semi-parametric models, with the effectiveness of the likelihood approach and good power properties. However, when the sample size is small or the dimension is high, the method is poorly calibrated, producing tests that generally have a higher type I error. In addition, it suffers from a limiting convex hull constraint. Many statisticians have proposed methods to address the performance. We explore the method proposed by Chen which makes an adjustment on empirical likelihood method. This thesis derives an adjusted empirical likelihood-based method for comparing two treatment effects in a linear model setting. We use the adjusted empirical likelihood-based method to make inference for the difference by comparing the parameters in two linear models. Our method is free of the assumptions of normally distributed and homogeneous errors, and equal sample size. In addition, the adjusted empirical likelihood method is Bartlett correctable. We apply the Bartlett correction procedure to further improve the coverage of our proposed method. Simulation experimental are used to illustrate that our method outperforms the published ones and also empirical likelihood-based method. This method can be extended into multiple treatment effects comparison.

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