Dimension reduction and predictor selection in semiparametric models

• 成果类型: Article
• 署名作者: Yu, Zhou; Zhu, Liping; Peng, Heng; Zhu, Lixing
• 署名单位: East China Normal University; Shanghai University of Finance & Economics; Hong Kong Baptist University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast005
• 发表日期: 2013
• 页码: 641654
• 关键词: sliced inverse regression; DANTZIG SELECTOR; CLASSIFICATION; shrinkage; likelihood

摘要

Dimension reduction in semiparametric regressions includes construction of informative linear combinations and selection of contributing predictors. To reduce the predictor dimension in semiparametric regressions, we propose an l(1)-minimization of sliced inverse regression with the Dantzig selector, and establish a non-asymptotic error bound for the resulting estimator. We also generalize the regularization concept to sliced inverse regression with an adaptive Dantzig selector. This ensures that all contributing predictors are selected with high probability, and that the resulting estimator is asymptotically normal even when the predictor dimension diverges to infinity. Numerical studies confirm our theoretical observations and demonstrate that our proposals are superior to existing estimators in terms of both dimension reduction and predictor selection.