Topics in high-dimensional asymptotics
Abstract/Contents
- Abstract
- Many multivariate statistics problems of current interest involve data with a large sample size and a large dimension. In this thesis we study several problems in this area. We work in the framework of high-dimensional asymptotics, where both the sample size and the dimension grow to infinity, such that their aspect ratio converges to a constant. In this setting, we leverage and further develop results from random matrix theory for the analysis of correlated multivariate data. Our first problem develops a fundamental new computational tool to numerically find the limiting empirical eigenvalue spectrum of sample covariance matrices. Our second problem uses this to develop new tests in PCA under local alternatives. Our third problem studies the problem of PCA from linearly modulated data, arising in missing data and deconvolution problems.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Dobriban, Edgar |
|---|---|
| Associated with | Stanford University, Department of Statistics. |
| Primary advisor | Donoho, David Leigh |
| Thesis advisor | Donoho, David Leigh |
| Thesis advisor | Johnstone, Iain |
| Thesis advisor | Owen, Art B |
| Advisor | Johnstone, Iain |
| Advisor | Owen, Art B |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Edgar Dobriban. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Edgar Dobriban
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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