THE FUSED KOLMOGOROV FILTER: A NONPARAMETRIC MODEL-FREE SCREENING METHOD
THE FUSED KOLMOGOROV FILTER: A NONPARAMETRIC MODEL-FREE SCREENING METHOD
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DOI：
10.1214/14-aos1303
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发表时间：
2015-08-01
影响因子：
4.5
通讯作者：
Zou, Hui
中科院分区：
文献类型：
--
作者：
Mai, Qing;Zou, Hui
提出了一种新的无模型筛选方法——融合Kolmogorov滤波器，用于高维数据分析。该方法是完全非参数的，可以处理多种类型的协变量和响应变量，包括连续变量、离散变量和分类变量。我们应用融合Kolmogorov滤波器来处理各种应用中出现的变量筛选问题，如多类分类、非参数回归和泊松回归等。结果表明，在弱正则性条件下，融合Kolmogorov滤波器具有可靠的筛选性能，比现有的许多非参数筛选方法所要求的条件温和得多。特别是，当协变量彼此强依赖时，融合的Kolmogorov滤波器仍然是强大的。通过仿真和实际数据示例进一步证明了融合Kolmogorov滤波器优于现有筛选方法的性能。
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.