Eigenvalues in multivariate random effects models
Abstract/Contents
- Abstract
- We study principal component analyses in multivariate random and mixed effects linear models. These models are commonly used in quantitative genetics to decompose the variation of phenotypic traits into consistuent variance components. Applications arising in evolutionary biology require understanding the eigenvalues and eigenvectors of these components in high-dimensional multivariate settings. However, these quantities may be difficult to estimate from limited samples when the number of traits is large. We describe several phenomena concerning sample eigenvalues and eigenvectors of classical MANOVA estimators in the presence of high-dimensional noise, including dispersion of the bulk eigenvalue distribution, bias and aliasing of outlier eigenvalues and eigenvectors, and Tracy-Widom fluctuations at the spectral edges. A common theme is that the spectral properties of the MANOVA estimate for one component may be influenced by the other components. In the setting of a simple spiked covariance model, we introduce alternative estimators for the leading eigenvalues and eigenvectors that correct for this problem in a high-dimensional asymptotic regime.
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 | 2018; ©2018 |
| Publication date | 2018; 2018 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Fan, Zhou |
|---|---|
| Degree supervisor | Johnstone, Iain |
| Degree supervisor | Montanari, Andrea |
| Thesis advisor | Johnstone, Iain |
| Thesis advisor | Montanari, Andrea |
| Thesis advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Degree committee member | Candès, Emmanuel J. (Emmanuel Jean) |
| Associated with | Stanford University, Department of Statistics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Zhou Fan. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis Ph.D. Stanford University 2018. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2018 by Zhou Fan
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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