Likelihood ratio testing in critically-spiked wigner models
Abstract/Contents
- Abstract
- Spiked random matrix models are widely used to model data in which a low-rank signal exists alongside high-dimensional noise. When the eigenvalues of this signal, known as spikes, are either above or below a certain critical threshold, the corresponding models have been widely studied and are well understood. However, the behavior of models with spikes at the critical threshold is more difficult to study, and has often remained elusive, despite the existence of data that is not well-explained by either sub- or supercritical models. This thesis contains the results of series of projects that investigate the likelihood ratios for Gaussian models with critical spikes. It includes rigorous results illustrating the transition between the qualitatively different sub- and supercritical regimes, which has applications not only in statistics, but also in the statistical physics of the SSK model for magnetism. It also contains edge universality results, demonstrating how the quantities crucial for understanding the likelihood of critically-spiked Gaussian random matrices can be extended to their Wigner counterparts. The thesis concludes with a presentation of results about phenomena occurring exactly at the critical threshold, determining the contiguous set of alternatives for testing a critical spike and providing the first description of the limiting likelihood ratio for such tests.
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 | 2022; ©2022 |
| Publication date | 2022; 2022 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Pavlyshyn, Damian Theodore |
|---|---|
| Degree supervisor | Johnstone, Iain |
| Thesis advisor | Johnstone, Iain |
| Thesis advisor | Dembo, Amir |
| Thesis advisor | Owen, Art B |
| Degree committee member | Dembo, Amir |
| Degree committee member | Owen, Art B |
| Associated with | Stanford University, Department of Statistics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Damian Pavlyshyn. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis Ph.D. Stanford University 2022. |
| Location | https://purl.stanford.edu/wy460rk5773 |
Access conditions
- Copyright
- © 2022 by Damian Theodore Pavlyshyn
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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