THE FUSED KOLMOGOROV FILTER: A NONPARAMETRIC MODEL-FREE SCREENING METHOD

• 成果类型: Article
• 署名作者: Mai, Qing; Zou, Hui
• 署名单位: State University System of Florida; Florida State University; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1303
• 发表日期: 2015
• 页码: 1471-1497
• 关键词: sliced inverse regression; variable selection; CLASSIFICATION; estimators; likelihood

摘要

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.