Eigenvalue shrinkage methods in high-dimensional estimation
Abstract/Contents
- Abstract
- This thesis studies applications of nonlinear eigenvalue shrinkage in high-dimensional estimation problems. We focus on applications in high-dimensional linear discriminant analysis and linear regression in the regime where the number of predictors and the sample size grow proportionately to infinity. Moreover, we study the problem of estimation of functions of large symmetric matrices in the presence of additive noise and provide an algorithm to approximate the optimally shrunk eigenvalues. We also study the problem of spectrum recovery, which serves as an intermediate step in the procedure that we describe.
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 | Lolas, Panagiotis |
|---|---|
| Degree supervisor | Johnstone, Iain |
| Degree supervisor | Ying, Lexing |
| Thesis advisor | Johnstone, Iain |
| Thesis advisor | Ying, Lexing |
| Thesis advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Degree committee member | Candès, Emmanuel J. (Emmanuel Jean) |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Panagiotis Lolas. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2022. |
| Location | https://purl.stanford.edu/ww849fd3178 |
Access conditions
- Copyright
- © 2022 by Panagiotis Lolas
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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