Applied statistical methods for high-dimensional generalized linear models
Abstract/Contents
- Abstract
- The Generalized Linear Model (GLM) is a fundamental statistical model to describe the relation between a response variable and a set of covariates. The model coefficients of a GLM are usually estimated using the maximum likelihood estimator (MLE) and confidence intervals for the coefficients are constructed using the classical asymptotic theory of the MLE. While the classical theory is valid under the condition that the number of variables p is vanishing compared to the number of observations n, it is invalid when p is comparable to n. To infer model parameters in the high-dimensional setting, researchers have been studying the asymptotic distribution of the MLE when p grows with n at a constant ratio, which they found to be informative in practical settings. These works typically focus on the setting when the covariates are i.i.d. or multivariate Gaussian. One open question is how to estimate the MLE distribution for general covariates. In this work, we study the distribution of the MLE with the objective of achieving valid inference for a high-dimensional GLM. We take two approaches in our study. First, we derive the theoretical distribution of a high-dimensional logistic regression when the covariates are multivariate Gaussian, and we demonstrate that our theory is accurate for moderate sample sizes. Second, when covariates are not Gaussian, we develop a resized bootstrap method to approximate the MLE distribution. We observe in simulated examples that the resized bootstrap method provides valid inference for a variety of GLM and covariate distributions. One application of our method is constructing confidence intervals for GLM coefficients.
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 | Zhao, Qian, (Researcher in applied statistical methods) |
|---|---|
| Degree supervisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Thesis advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Thesis advisor | Montanari, Andrea |
| Thesis advisor | Taylor, Jonathan E |
| Degree committee member | Montanari, Andrea |
| Degree committee member | Taylor, Jonathan E |
| Associated with | Stanford University, Department of Statistics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Qian Zhao. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/wc409cq6066 |
Access conditions
- Copyright
- © 2021 by Qian Zhao
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