Topics in exact asymptotics for high-dimensional regression
Abstract/Contents
- Abstract
- Exact asymptotic theory refers to a collection of techniques for precisely characterizing the distribution of high-dimensional regression estimators. Examples of the estimators it characterizes include the Lasso, ridge regression, the elastic net, and SLOPE, among others. The theory requires strong assumptions---Gaussian and sometimes independent covariates---and is usually developed for one restricted class of estimators at a time. This thesis expands the scope of exact asymptotic theory by providing generalizations to symmetric but possibly non-separable penalties with independent covariates and to correlated covariates in the context of the Lasso. Further, it provides novel exact asymptotic characterizations of the joint distribution of two regression estimators computed on the same data. It applies these developments and existing theory to important statistical problems, including optimal penalty design, adaptive estimation, inference with the debiased Lasso, hyperparameter tuning, and consistent estimation of low-dimensional parameters when high-dimensional nuisance parameters cannot be estimated well.
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 | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Celentano, Michael Vincent |
|---|---|
| Degree supervisor | Montanari, Andrea |
| Thesis advisor | Montanari, Andrea |
| Thesis advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Thesis advisor | Donoho, David Leigh |
| Degree committee member | Candès, Emmanuel J. (Emmanuel Jean) |
| Degree committee member | Donoho, David Leigh |
| Associated with | Stanford University, Department of Statistics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Michael Celentano. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/hr472kk9683 |
Access conditions
- Copyright
- © 2021 by Michael Vincent Celentano
- License
- This work is licensed under a Creative Commons Attribution 3.0 Unported license (CC BY).
Also listed in
Loading usage metrics...