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December 2009 Structured variable selection and estimation
Ming Yuan, V. Roshan Joseph, Hui Zou
Ann. Appl. Stat. 3(4): 1738-1757 (December 2009). DOI: 10.1214/09-AOAS254


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.


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Ming Yuan. V. Roshan Joseph. Hui Zou. "Structured variable selection and estimation." Ann. Appl. Stat. 3 (4) 1738 - 1757, December 2009.


Published: December 2009
First available in Project Euclid: 1 March 2010

zbMATH: 1184.62032
MathSciNet: MR2752156
Digital Object Identifier: 10.1214/09-AOAS254

Keywords: Effect heredity , nonnegative garrote , quadratic programming , regularization , Variable selection

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.3 • No. 4 • December 2009
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