Problems in change-point detection
Abstract/Contents
- Abstract
- This thesis discusses two projects about change-point detection problems. The first part of the thesis focuses on the comparison between the higher-criticism and the Berk-Jones statistics, both of which belong to an optimal sub-class among a larger class of statistics for testing Gaussian mixture models. Despite the asymptotic equivalence in the power, we heuristically compare the power of them by considering the rejection regions under nite sample settings, followed by numerical simulations that verify the argument. We deduce and prove the approximate formula for the tail probabilities of these two statistics, with which one can efficiently determine the threshold for any specific significance level (that is, the probability of getting a false positive). A slight generation of the derivation provides the formula for computing the power of both statistics under Gaussian mixture alternatives. Besides, we explore two applications of the problem: construction of a lower confidence bound for the proportion of the false null hypothesis and copy number variation detection in aligned DNA sequences. The second project is concerned with change-point detection in a stochastic process. The project is motivated by the Chernobyl disaster, which occurred in 1986. The general scientific question was whether radioactive fallout from the disaster had an impact on human health, specifically the viability of human fetuses, in southern Germany. Professor H. R. Lerche of the University of Freiburg provided data from 1980/01/01 to 1996/12/31 on live births and still births in several regions of southern Germany. We model the probability of stillbirths with a logistic model, and test if there is a change-point in the intercept after the accident. We derive approximations for the overall p-value of the test statistic by two different methods and compare them with numerical experiments to assess their performance. Finally we apply out method to the data, which do not provide sufficient evidence to infer an impact of the accident, in agreement with the results of previous studies.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Li, Jian |
|---|---|
| Associated with | Stanford University, Department of Statistics. |
| Primary advisor | Siegmund, David, 1941- |
| Thesis advisor | Siegmund, David, 1941- |
| Thesis advisor | Lai, T. L |
| Thesis advisor | Walther, Guenther |
| Advisor | Lai, T. L |
| Advisor | Walther, Guenther |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jian Li. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Jian Li
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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