Variable selection and classification by the GRIDprocedure

We describe a method for variable selection and classification for a non-parametric regression in high dimensions where only a relatively small subset ofvariables are relevant and may have nonlinear effects on the response. The newmethod, called the GRID, is proposed and deeply investigated in a forthcoming pa-per. It is an extension of the RODEO method of [3] (which only makes variableselection). Among the novelties of our procedure, a graphical tool for identifyingthe low dimensional nonlinear structure of the regression function is shown. Giventhe lenght of this paper, we briefly describe the method and present the theoreticalfoundations and simulation performance of only the first stage of the procedure (i.e.,variable selection and linear/nonlinear classification).