Local Polynomials for Variable Selection

Abstract

Nonparametric estimators are particularly affected by the curse of dimensionality. An interesting method has been proposed recently, the RODEO, which uses the nonparametric local linear estimator for high dimensional regression, avoiding the curse of dimensionality when the model is sparse. This method can be used for variable selection as well, but it is blind to linear dependencies. For this reason, it is suggested to use the RODEO on the residuals of a LASSO. In this paper we propose an alternative solution, based on the adaptation of the well-known asymptotic results for the local linear estimator. The proposal can be used to complete the RODEO, avoiding the necessity of filtering the data through the LASSO. Some theoretical properties and the results of a simulation study are shown.