Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors

In this paper we consider a nonparametric regression model that admits a mix of continuous and discrete regressors, some of which may in fact be redundant (that is, irrelevant). We show that, asymptotically, a data-driven least squares cross-validation method can remove irrelevant regressors. Simulations reveal that this "automatic dimensionality reduction" feature is very effective in finite-sample settings. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.