STRUCTURED VARIABLE SELECTION AND ESTIMATION

• 成果类型: Article
• 署名作者: Yuan, Ming; Joseph, V. Roshan; Zou, Hui
• 署名单位: University System of Georgia; Georgia Institute of Technology; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/09-AOAS254
• 发表日期: 2009
• 页码: 1738-1757
• 关键词: designed experiments; regression; models

摘要

In linear regression problems with related predictors, it is desirable to do variable selection and estimation by maintaining the hierarchical or structural relationships among predictors. In this paper we propose non-negative garrote methods that can naturally incorporate such relationships defined through effect heredity principles or marginality principles. We show that the methods are very easy to compute and enjoy nice theoretical properties. We also show that the methods can be easily extended to deal with more general regression problems such as generalized linear models. Simulations and real examples are used to illustrate the merits of the proposed methods.