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Statistical Inference for Change Points in High-Dimensional Offline and Online Data

Li, Lingjun
http://rave.ohiolink.edu/etdc/view?acc_num=kent1586206330858843

Abstract Details

2020, PHD, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
High-dimensional offline and online time series data are characterized by a large number of measurements and complex dependence, and often involve change points. Change point detection in offline time series data improves the parameter testing and estimation by pooling homogeneous observations between two successive change points. Change point detection in online time series data provides timely snapshots of the monitored system and allows for real-time anomaly detection. Despite its importance, methods available for change point detection in high-dimensional offline and online time series data are scarce. In the first part of the thesis, we present some new statistics for change-point testing and estimation in high dimensional offline time series data. We establish their theoretical properties including asymptotic distributions and consistency under mild conditions. The developed new methods are non-parametric without imposing restrictive structural assumptions. They incorporate spatial and temporal dependence in data. Most importantly, they can detect the change point near the boundary of time series data. In the second part of the thesis, we extend these new statistics to high-dimensional online time series data and provide a new stopping rule to detect a change point as early as possible after an anomaly occurs. We study theoretical properties of the new stopping rule, and derive an explicit expression for the average run length (ARL) so that the level of threshold in the stopping rule can be easily obtained with no need to run time-consuming Monte Carlo simulations. We also establish an upper bound for the expected detection delay (EDD), which demonstrates the impact of data dependence and magnitude of structure change in data. Simulation and case studies are provided to demonstrate the empirical performance of the proposed offline and online change-point detection methods.
Jun Li (Advisor)
Mohammad Khan (Committee Member)
Jing Li (Committee Member)
Cheng-Chang Lu (Committee Member)
Ruoming Jin (Committee Member)
135 p.
Mathematics; Statistics
Change point analysis; Change-point detection; Spatial-temporal data; Large p small n; High-dimensional data; Average run length; Expected detection delay

Recommended Citations

Citations

  • Li, L. (2020). Statistical Inference for Change Points in High-Dimensional Offline and Online Data [Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1586206330858843

    APA Style (7th edition)

  • Li, Lingjun. Statistical Inference for Change Points in High-Dimensional Offline and Online Data. 2020. Kent State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1586206330858843.

    MLA Style (8th edition)

  • Li, Lingjun. "Statistical Inference for Change Points in High-Dimensional Offline and Online Data." Doctoral dissertation, Kent State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1586206330858843

    Chicago Manual of Style (17th edition)

kent1586206330858843
377
© 2020, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.