Indirect multivariate response linear regression

• 成果类型: Article
• 署名作者: Molstad, Aaron J.; Rothman, Adam J.
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw034
• 发表日期: 2016
• 页码: 595607
• 关键词: covariance-matrix estimation; Dimension Reduction; maximum-likelihood; variable selection; breast-cancer; prediction; models; Lasso

摘要

We propose a class of estimators of the multivariate response linear regression coefficient matrix that exploits the assumption that the response and predictors have a joint multivariate normal distribution. This allows us to indirectly estimate the regression coefficient matrix through shrinkage estimation of the parameters of the inverse regression, or the conditional distribution of the predictors given the responses. We establish a convergence rate bound for estimators in our class and we study two examples, which respectively assume that the inverse regression's coefficient matrix is sparse and rank deficient. These estimators do not require that the forward regression coefficient matrix is sparse or has small Frobenius norm. Using simulation studies, we show that our estimators outperform competitors.