Dissertation
Non-nested Hypothesis Tests for Vine Copulas and Statistical Learning Techniques in Process Monitoring
Doctor of Philosophy (PhD), Washington State University
01/2019
Handle:
https://hdl.handle.net/2376/112102
Abstract
In this dissertation, we first introduce three bootstrap-based non-nested hypothesis tests for regular vine-copulas. These test statistics are derived from log-likelihood ratio test statistics and Cox test statistics. This study presents the power study comparing the proposed tests with existing vine-copula non-nested hypothesis tests. Across models with varying structures of regular copulas, our hypothesis tests consistently achieve higher power. Deriving from statistical algorithms, we also propose two different control charts that can be applied to multivariate statistical process control (MSPC). The first one is based on support vector data description (SVDD). We propose a SVDD control chart using the Mahalanobis distance kernel (Mahalanobis k-chart). Mathematical illustrations and statistical comparisons are presented on the basis of both simulations and a real example of electricity consumption. The results show that Mahalanobis k-chart can achieve lower Phase II average run length (ARL) in most shifted-process scenarios. Another control chart we propose is random oversampling gradient boosting real-time contrasts (ROGB-RTC) chart. Real-time contrasts (RTC) control charts convert the statistical process monitoring problem into a dynamic binary classification problem. But only a limited number of RTC studies have scrutinized the imbalance problem between the sample size of the reference data and that of the sliding window data. Our control chart handles the imbalance problem in terms of both classifier and monitoring statistics. Experiments show that the proposed method achieves better performance than that of the original real-time contrasts chart.
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Details
- Title
- Non-nested Hypothesis Tests for Vine Copulas and Statistical Learning Techniques in Process Monitoring
- Creators
- Ziyi Chen
- Contributors
- Francis Pascual (Advisor)Haijun Li (Committee Member)Marc Evans (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 112
- Identifiers
- 99900581617201842
- Language
- English
- Resource Type
- Dissertation