Change-point detection in mean and variance or both

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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.


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


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


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.

Access conditions

© 2023 by Zhen Zhu
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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