  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.
