Detection of multiple change-points : sequential testing and model selection
Abstract/Contents
- Abstract
- In this thesis, we consider the problem of estimating the number of change-points and their locations in a process. In the first part of the thesis, we focus on a sequence of non Gaussian observations with changing mean values. Motivated by the heavy tail, Laplace-like data in the array based experiments, we derive a score-like statistic for testing whether the mean changes or not in Laplace data in Chapter 2. We then generalize this test statistic to a class of non-parametric test statistics and apply these robust statistics to detect change-points in array based data. In Chapter 3, we consider the abrupt mean change problem in the one parameter exponential family data. With the assumption that the number of change is unbounded, we derive a modified BIC to determine the number of change-points in the sequence and apply our method to detect DNA copy number changes in sequencing data. This modified BIC connects naturally to the second part of the thesis, where we consider model selection of smooth change-point models. In Chapter 4, we investigate the segmented line regression model and propose a slightly different smooth change-point problem. We derive a modified BIC for the smooth problem based on the Laplace's method. Because irregularities in the likelihood function vanish after smoothing, the derivation of this modified BIC is similar to the classic BIC. In the last chapter, we extend the modified BIC to other change-point problems.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Liu, Yi |
|---|---|
| Associated with | Stanford University, Department of Statistics. |
| Primary advisor | Siegmund, David, 1941- |
| Thesis advisor | Siegmund, David, 1941- |
| Thesis advisor | Walther, Guenther |
| Thesis advisor | Zhang, Nancy R. (Nancy Ruonan) |
| Advisor | Walther, Guenther |
| Advisor | Zhang, Nancy R. (Nancy Ruonan) |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Yi Liu. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2013. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Yi Liu
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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