A nonparametric procedure for linear and nonlinear variable screening

A new model-free screening method, called Derivative Empirical Likelihood Independent Screening (D-ELSIS), is proposed for high-dimensional regression analysis. Without requiring a specific parametric form of the underlying model, our method is able to identify explanatory variables that contribute to the explanation of the response variable in nonparametric and non-additive contexts. In addition, with our method we are also able to identify the relevant variables that have a nonlinear effect on the response variable. This approach is fully nonparametric and combines the estimation of the first marginal derivatives by the local polynomial estimator together with the empirical likelihood technique. Our approach can handle a dimensionality that grows exponentially with the sample size. We report some simulation results and a real data example to show that the D-ELSIS screening approach performs satisfactorily, compared with the most direct competitors.