On the adaptive elastic-net with a diverging number of parameters

Details On the adaptive elastic-net with a diverging number of parameters On the adaptive elastic-net with a diverging number of parameters

2009-08-13

arxiv.org/abs/0908.1836v1

Annals of Statistics 2009, Vol. 37, No. 4, 1733-1751

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-AOS625 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/08-AOS625

We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property [J. Amer. Statist. Assoc. 96 (2001) 1348--1360] and [Ann. Statist. 32 (2004) 928--961] which ensures the optimal large sample performance. Furthermore, the high-dimensionality often induces the collinearity problem, which should be properly handled by the ideal method. Many existing variable selection methods fail to achieve both goals simultaneously. In this paper, we propose the adaptive elastic-net that combines the strengths of the quadratic regularization and the adaptively weighted lasso shrinkage. Under weak regularity conditions, we establish the oracle property of the adaptive elastic-net. We show by simulations that the adaptive elastic-net deals with the collinearity problem better than the other oracle-like methods, thus enjoying much improved finite sample performance.

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