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The varying-coefficient model is an important nonparametric statistical modelthat allows us to examine how the effects of covariates vary with exposurevariables. When the number of covariates is big, the issue of variableselection arrives. In this paper, we propose and investigate marginalnonparametric screening methods to screen variables in ultra-high dimensionalsparse varying-coefficient models. The proposed nonparametric independencescreening (NIS) selects variables by ranking a measure of the nonparametricmarginal contributions of each covariate given the exposure variable. The sureindependent screening property is established under some mild technicalconditions when the dimensionality is of nonpolynomial order, and thedimensionality reduction of NIS is quantified. To enhance practical utility andthe finite sample performance, two data-driven iterative NIS methods areproposed for selecting thresholding parameters and variables: conditionalpermutation and greedy methods, resulting in Conditional-INIS and Greedy-INIS.The effectiveness and flexibility of the proposed methods are furtherillustrated by simulation studies and real data applications.

Nonparametric Independence Screening in Sparse Ultra-High Dimensional Varying Coefficient Models