Change-point detection in mean and variance or both
Abstract/Contents
- Abstract
- The focus of this thesis is on developing statistical methods to identify change-points in datasets where there may be changes in both mean and variance. We propose novel statistical methods for detecting such change-points and discuss both type-I error approximations and power evaluations. Our first set of tests is based on score statistics for the single change-point problems and introduces a hyper-parameter to allow flexibility between change in the mean parameter and change in the variance parameter. We also introduce both box-type and ellipse-type statistics based on different shapes of the rejection region. Analyzing the score-based statistics is challenging due to the heavier than normal tails in the $\chi^2$ distribution in the variance component of the statistics. We develop theoretical methods that deal with this difficulty when approximating type-I error. Additionally, we provide marginal power calculations for assessing the effectiveness of these tests. The required modifications for both type-I error approximations and marginal power calculations for the interval change problems are discussed as well. Next, we propose tests based on the full generalized likelihood statistics and the box-type and ellipse-type statistics with the same hyper-parameter as in the score case. The theoretical results for this set of tests are simpler than the score tests because now both mean and variance components of our statistics are approximately Gaussian distributed. We provide type-I error approximations and marginal power calculations for the full generalized likelihood statistics in both single change-point and the interval change problems. Finally, we compare the power of all these statistics with the power of the classical change-point statistics which only allow change in the mean and assume variance is constant. We also examine some real-world datasets to demonstrate the effectiveness and pitfalls of these statistics.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2023; ©2023 |
| Publication date | 2023; 2023 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Zhu, Zhen, (Researcher in statistics) |
|---|---|
| Degree supervisor | Siegmund, David, 1941- |
| Thesis advisor | Siegmund, David, 1941- |
| Thesis advisor | Lai, T. L |
| Thesis advisor | Linderman, Scott |
| Degree committee member | Lai, T. L |
| Degree committee member | Linderman, Scott |
| Associated with | Stanford University, School of Humanities and Sciences |
| Associated with | Stanford University, Department of Statistics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Zhen Zhu. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis Ph.D. Stanford University 2023. |
| Location | https://purl.stanford.edu/tf277nz3560 |
Access conditions
- Copyright
- © 2023 by Zhen Zhu
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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