High-dimensional variable selection

Details High-dimensional variable selection High-dimensional variable selection

2007-04-09

arxiv.org/abs/0704.1139v2

Annals of Statistics 2009, Vol. 37, No. 5A, 2178-2201

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-AOS646 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/08-AOS646

This paper explores the following question: what kind of statistical guarantees can be given when doing variable selection in high-dimensional models? In particular, we look at the error rates and power of some multi-stage regression methods. In the first stage we fit a set of candidate models. In the second stage we select one model by cross-validation. In the third stage we use hypothesis testing to eliminate some variables. We refer to the first two stages as "screening" and the last stage as "cleaning." We consider three screening methods: the lasso, marginal regression, and forward stepwise regression. Our method gives consistent variable selection under certain conditions.

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