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Dissertation
A Novel Approach to Multiple Hypothesis Testing Under Dependence and Insights for Inference on Random Dot Product Networks
Washington State University
Doctor of Philosophy (PhD), Washington State University
2023
DOI:
https://doi.org/10.7273/000005305
Abstract
Statistical inference problems, particularly in the context of multiple hypotheses testing, attract extensive research attention. This is particularly true when the test candidates exhibit interdependence or lack of independence among themselves. Concurrently, network analysis has emerged as a pivotal field for unveiling the interconnectedness and relationships among entities within a network, also making it a prominent area of investigation. In this dissertation, we investigate two distinct topics. In the first study, we introduce the concept of "r-Power" for evaluating multiple hypothesis testing under dependence, with our focus being on block diagonal correlation correlation structure. We explore its asymptotic properties and validate our findings through comprehensive simulation studies. Additionally, we present an algorithm that effectively utilizes this metric and demonstrate its practical applications in gene co-expression and Genome-Wide Association Studies (GWAS). Our results illustrate that, in a high-dimensional data, with relatively low number of signals, our method is able to provide a confidence to the list of captured signals. Furthermore, our formulation offers insights into selecting an appropriate number of test candidates for improved confidence levels. In our second study, we focus on statistical inferential techniques tailored for social network data, with a specific emphasis on the Random Dot Product model. We address the challenge of overestimation or underestimation of common social network metrics under this model with adjacency spectral embedding, particularly for small to medium-scaled networks. Additionally, we propose a novel embedding method for accurately representing such networks asymptotically and determine graph embedding for specific graph families. We also reviewed hypotheses testing for social network comparison and proposed a parametric approach to test the difference between two social networks. We validate our findings using data from a village social network. Overall, this dissertation contributes to our understanding of statistical inference in high-dimensional data, with our focus on multiple hypotheses testing and network analysis. It tackles challenges, presents solutions, and showcases practical applications, thereby enhancing our overall knowledge in these areas.
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Details
- Title
- A Novel Approach to Multiple Hypothesis Testing Under Dependence and Insights for Inference on Random Dot Product Networks
- Creators
- Swarnita Chakraborty
- Contributors
- Nairanjana Dasgupta (Advisor)Daryl Deford (Committee Member)Yuan Wang (Committee Member)Zhiwu Zhang (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 183
- Identifiers
- 99901031138801842
- Language
- English
- Resource Type
- Dissertation