A Note on High-Dimensional Linear Regression With Interactions

The problem of interaction selection in high-dimensional data analysis has recently received much attention. This note aims to address and clarify several fundamental issues in interaction selection for linear regression models, especially when the input dimension p is much larger than the sample size n. We first discuss how to give a formal definition of "importance" for main and interaction effects. Then we focus on two-stage methods, which are computationally attractive for high-dimensional data analysis but thus far have been regarded as heuristic. We revisit the counterexample of Turlach and provide new insight to justify two-stage methods from the theoretical perspective. In the end, we suggest new strategies for interaction selection under the marginality principle and provide some simulation results.NSF [DMS-1309507, DMS-1418172]; [NSFC-11571009]12 month embargo; published online: 15 December 2016This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu