# A doubly sparse approach for group variable selection

A doubly sparse approach for group variable selection We propose a new penalty called the doubly sparse (DS) penalty for variable selection in high-dimensional linear regression models when the covariates are naturally grouped. An advantage of the DS penalty over other penalties is that it provides a clear way of controlling sparsity between and within groups, separately. We prove that there exists a unique global minimizer of the DS penalized sum of squares of residuals and show how the DS penalty selects groups and variables within selected groups, even when the number of groups exceeds the sample size. An efficient optimization algorithm is introduced also. Results from simulation studies and real data analysis show that the DS penalty outperforms other existing penalties with finite samples. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of the Institute of Statistical Mathematics Springer Journals

# A doubly sparse approach for group variable selection

, Volume 69 (5) – Jun 28, 2016
29 pages

/lp/springer_journal/a-doubly-sparse-approach-for-group-variable-selection-ZXtycYorFM
Publisher
Springer Japan
Subject
Statistics; Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance
ISSN
0020-3157
eISSN
1572-9052
D.O.I.
10.1007/s10463-016-0571-z
Publisher site
See Article on Publisher Site

### Abstract

We propose a new penalty called the doubly sparse (DS) penalty for variable selection in high-dimensional linear regression models when the covariates are naturally grouped. An advantage of the DS penalty over other penalties is that it provides a clear way of controlling sparsity between and within groups, separately. We prove that there exists a unique global minimizer of the DS penalized sum of squares of residuals and show how the DS penalty selects groups and variables within selected groups, even when the number of groups exceeds the sample size. An efficient optimization algorithm is introduced also. Results from simulation studies and real data analysis show that the DS penalty outperforms other existing penalties with finite samples.

### Journal

Annals of the Institute of Statistical MathematicsSpringer Journals

Published: Jun 28, 2016

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