Edgeworth approximations for spiked PCA models and applications
Abstract/Contents
- Abstract
- We study improved approximations to the distributions of the largest eigenvalues of the sample covariance matrix of i.i.d. zero-mean Gaussian random vectors, in the high-dimensional regime where the ratio of the dimension of each observation to the number of observations converges to a positive constant. Assuming that a fixed number of population principal components have "supercritical" variances and that the remaining noise components have common variance 1, we derive Edgeworth corrections to the limiting Gaussian distributions of the supercritical sample eigenvalues. The Edgeworth correction involves a quadratic polynomial, as in classical settings, but the coefficients reflect the high-dimensional structure and exhibit the repulsion between supercritical eigenvalues. The methods involve Edgeworth expansions for sums of independent non-identically distributed variates obtained by conditioning on the other sample eigenvalues, and the limiting bulk properties and fluctuations of these eigenvalues. As an application, we consider post-selective inference for supercritical eigenvalues. Empirical study shows that Edgeworth approximations can improve the inference, along with a better asymptotic accuracy guarantee than the normal approximation.
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 | 2019; ©2019 |
| Publication date | 2019; 2019 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Yang, Jeha |
|---|---|
| Degree supervisor | Johnstone, Iain |
| Thesis advisor | Johnstone, Iain |
| Thesis advisor | Donoho, David Leigh |
| Thesis advisor | Owen, Art B |
| Degree committee member | Donoho, David Leigh |
| Degree committee member | Owen, Art B |
| Associated with | Stanford University, Department of Statistics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Jeha Yang. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis Ph.D. Stanford University 2019. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2019 by Jeha Yang
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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