Factor analysis for high dimensional data
Abstract/Contents
- Abstract
- Factor analysis is a powerful dimension reduction tool with explicit statistical model and assumptions. It assumes that the data matrix can be decomposed as linear combinations of latent factors plus independent noise which has heteroscedastic variances for each variable. This dissertation provides two approaches estimating the factor analysis model for high-dimensional data and an application of factor analysis to confounder adjustment in high-throughput genetics experiments. One approach, BCV-ESA, uses an early stopping iterative algorithm to estimate the model and a bi-cross-validation technique to select the number of factors to retain. The other approach, POT-S, starts with a joint convex optimization using perspective transformation and nuclear penalty and estimates the tuning parameter by a Wold-style cross-validation. Both methods are superior to previous methods in the accuracy of estimating the weak factors and the noise variances. For the confounder adjustment application, the mathematical properties of a two-step algorithm estimating the individual effects of the primary variable after confounding factors adjustment has been carefully studied. It is shown that under regularity conditions, the estimators of the individual effects can asymptotically achieve an oracle efficiency and eliminate bias or correlations in the p-values of individual effects.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2016 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Wang, Jingshu |
|---|---|
| Associated with | Stanford University, Department of Statistics. |
| Primary advisor | Owen, Art B |
| Thesis advisor | Owen, Art B |
| Thesis advisor | Walther, Guenther |
| Thesis advisor | Wong, Wing Hung |
| Advisor | Walther, Guenther |
| Advisor | Wong, Wing Hung |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jingshu Wang. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2016. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2016 by Jingshu Wang
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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