Author ORCID Identifier
Date of Award
Doctor of Philosophy (PhD)
Mathematics and Statistics
The empirical likelihood (EL), introduced by Owen (1988, 1990), is a powerful tool for constructing confidence intervals in nonparametric settings. Significant developments based on empirical likelihood have been made in recent years. In this dissertation, we investigate the performance of two extensions of EL, sample empirical likelihood (Chen and Kim, 2014) and Bayesian jackknife empirical likelihood (Cheng and Zhao, 2019) approaches, for several statistical problems.
One effective way to conduct statistical disclosure control is to use scrambled responses. Scrambled responses can be generated by using a controlled random device. We propose using the sample empirical likelihood approach to conduct statistical inference (using a Wilk-type confidence interval) under a complex survey design with scrambled responses.
Missing data, which are common in a variety of fields, reduce the representativeness of the sample and can lead to inference problems. We apply the Bayesian jackknife empirical likelihood method for inference with missing data and causal inference. The semiparametric fractional imputation estimator, proposed by Chen and Kim (2017), propensity score weighted estimator, and doubly robust estimator were used for inference with missing data.
The partial area under the receiver operating characteristic curve (pAUC) is a measure of diagnostic test performance. We propose using Bayesian jackknife empirical likelihood for inference for the pAUC and comparison of two tests.
Extensive simulation studies are conducted to compare the performance in terms of the coverage rate and average length of confidence interval between proposed methods and normal approximation/jackknife empirical likelihood methods. Furthermore, we demonstrate the application of the proposed approaches using real datasets.
Wang, Yuke, "Sample Empirical Likelihood under Complex Survey Design and Bayesian Jackknife Empirical Likelihood-based Inference for Missing Data and Partial AUC." Dissertation, Georgia State University, 2023.
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