Structured variable selection and estimation

Details Structured variable selection and estimation Structured variable selection and estimation

2010-11-02

arxiv.org/abs/1011.0610v1

Annals of Applied Statistics 2009, Vol. 3, No. 4, 1738-1757

Statistics

Applications

Published in at http://dx.doi.org/10.1214/09-AOAS254 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

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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