Sparse Multivariate Reduced-Rank Regression with Covariance Estimation

Author: 
Date created: 
2016-12-14
Identifier: 
etd9911
Keywords: 
Multivariate Regression
Reduced-Rank
Covariance Estimation
Variable Selection
LASSO
Simulation
Abstract: 

Multivariate multiple linear regression is multiple linear regression, but with multiple responses. Standard approaches assume that observations from different subjects are uncorrelated and so estimates of the regression parameters can be obtained through separate univariate regressions, regardless of whether the responses are correlated within subjects. There are three main extensions to the simplest model. The first assumes a low rank structure on the coefficient matrix that arises from a latent factor model linking predictors to responses. The second reduces the number of parameters through variable selection. The third allows for correlations between response variables in the low rank model. Chen and Huang propose a new model that falls under the reduced-rank regression framework, employs variable selection, and estimates correlations among error terms. This project reviews their model, describes its implementation, and reports the results of a simulation study evaluating its performance. The project concludes with ideas for further research.

Document type: 
Graduating extended essay / Research project
Rights: 
This thesis may be printed or downloaded for non-commercial research and scholarly purposes. Copyright remains with the author.
File(s): 
Supervisor(s): 
Jinko Graham
Department: 
Science: Department of Statistics and Actuarial Science
Thesis type: 
(Project) M.Sc.
Statistics: