High-dimensional multivariate regression and reduced rank estimators
Abstract/Contents
- Abstract
- In statistical learning and modeling, when the dimension of the data is higher than the number of samples, the estimation accuracy can be very poor and thus the model can be hard to interpret. One approach to reducing the dimension is based on the assumption that many variables are a nuisance and redundant; consequently, many variable selection methods have been proposed to identify only the most important variables. Another approach to reducing the dimension is factor extraction, which is based on the assumption that the high-dimensional data can be approximately projected on a lower-dimensional space. Factor extraction, such as principal component analysis (PCA) and canonical correlation analysis (CCA), provides a good interpretation of the data, but the dimension of the reduced space (the number of underlying features) is typically not easy to estimate. In the context of regression analysis, where we want to fit a linear model yt = BTxt + et given n observations xi 2 Rp and yi 2 Rq for i = 1; : : : ; n, several important variable selection methods, e.g. lasso-type shrinkage, forward stepwise selection and backward elimination, have been well studied for dimension reduction. However, there are not many theoretical results of these methods for multivariate regression models with stochastic regressors (also called 'stochastic regression models') found in the literature. In this dissertation, we present an effcient algorithm for solving high-dimensional multivariate linear stochastic regression. The motivation comes from modeling and prediction for multivariate time series models in macroeconomics and for linear MIMO (multiple-input and multiple-output) stochastic systems in control theory. By extending the 'orthogonal greedy algorithm' and 'high-dimensional information criterion' for 'weakly sparse' models in Ing and Lai (2011), we can choose a subset of xt and reduce the dimension p to o(n). We can then perform reduced-rank regression of yt on this reduced set of regressors and introduce an information criterion to choose the number of factors and estimate the factors. We provide theoretical results for our algorithm. We carry out simulation studies and an econometric data analysis to evaluate the algorithm.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Tsang, Ka Wai |
|---|---|
| Associated with | Stanford University, Department of Computational and Mathematical Engineering. |
| Primary advisor | Lai, T. L |
| Thesis advisor | Lai, T. L |
| Thesis advisor | Rajaratnam, Balakanapathy |
| Thesis advisor | Saunders, Michael A |
| Advisor | Rajaratnam, Balakanapathy |
| Advisor | Saunders, Michael A |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Ka Wai Tsang. |
|---|---|
| Note | Submitted to the Department of Computational and Mathematical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Ka Wai Tsang
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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