  The varying-coefficient model is an important nonparametric statistical model
that allows us to examine how the effects of covariates vary with exposure
variables. When the number of covariates is big, the issue of variable
selection arrives. In this paper, we propose and investigate marginal
nonparametric screening methods to screen variables in ultra-high dimensional
sparse varying-coefficient models. The proposed nonparametric independence
screening (NIS) selects variables by ranking a measure of the nonparametric
marginal contributions of each covariate given the exposure variable. The sure
independent screening property is established under some mild technical
conditions when the dimensionality is of nonpolynomial order, and the
dimensionality reduction of NIS is quantified. To enhance practical utility and
the finite sample performance, two data-driven iterative NIS methods are
proposed for selecting thresholding parameters and variables: conditional
permutation and greedy methods, resulting in Conditional-INIS and Greedy-INIS.
The effectiveness and flexibility of the proposed methods are further
illustrated by simulation studies and real data applications.
