The fused Kolmogorov filter: A nonparametric model-free screening method

Qing Mai, Hui Zou

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

A new model-free screening method called the fused Kolmogorov filter is proposed for high-dimensional data analysis. This new method is fully nonparametric and can work with many types of covariates and response variables, including continuous, discrete and categorical variables. We apply the fused Kolmogorov filter to deal with variable screening problems emerging from a wide range of applications, such as multiclass classification, nonparametric regression and Poisson regression, among others. It is shown that the fused Kolmogorov filter enjoys the sure screening property under weak regularity conditions that are much milder than those required for many existing nonparametric screening methods. In particular, the fused Kolmogorov filter can still be powerful when covariates are strongly dependent on each other. We further demonstrate the superior performance of the fused Kolmogorov filter over existing screening methods by simulations and real data examples.

Original languageEnglish (US)
Pages (from-to)1471-1497
Number of pages27
JournalAnnals of Statistics
Volume43
Issue number4
DOIs
StatePublished - Aug 1 2015

Keywords

  • High-dimensional data
  • Sure screening property
  • Variable screening

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