Structured variable selection and estimation

Ming Yuan, V. Roshan Joseph, Hui Zou

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1738-1757
Number of pages20
JournalAnnals of Applied Statistics
Issue number4
StatePublished - Dec 2009


  • Effect heredity
  • Nonnegative garrote
  • Quadratic programming
  • Regularization
  • Variable selection


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