Abstract: We consider the problem of estimating a relationship using semiparametric additive regression splines when there exist both continuous and categorical regressors, some of which are irrelevant but this is not known a priori. We show that choosing the spline degree, number of subintervals, and bandwidths via cross-validation can automatically remove irrelevant regressors, thereby delivering `automatic dimension reduction' without the need for pre-testing. Theoretical underpinnings are provided, finite-sample performance is studied, and an illustrative application demonstrates the efficacy of the proposed approach in finite-sample settings. An R package implementing the methods is available from the Comprehensive R Archive Network (Racine and Nie (2011)).
Key words and phrases: B-spline, discrete, kernel.