Abstract
Variable screening techniques have been proposed to mitigate the impact of high dimensionality in classification problems, including t-test marginal screening (Fan & Fan, 2008) and maximum marginal likelihood screening (Fan & Song, 2010). However, these methods rely on strong modelling assumptions that are easily violated in real applications. To circumvent the parametric modelling assumptions, we propose a new variable screening technique for binary classification based on the Kolmogorov-Smirnov statistic. We prove that this so-called Kolmogorov filter enjoys the sure screening property under much weakened model assumptions. We supplement our theoretical study by a simulation study.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 229-234 |
| Number of pages | 6 |
| Journal | Biometrika |
| Volume | 100 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 2013 |
Bibliographical note
Funding Information:The authors thank the editor and two referees for their helpful comments and suggestions. This work is supported in part by a grant from the National Science Foundation, U.S.A.
Keywords
- Dvoretzky-Kiefer-Wolfowitz inequality
- Kolmogorov-Smirnov test
- Sure screening property