Uniform convergence rates and automatic variable selection in nonparametric regression with functional and categorical covariates

Abstract

In Selk, L., and Gertheiss, J. [(2022), ‘Nonparametric Regression and Classification with Functional, Categorical, and Mixed Covariates’, Advances in Data Analysis and Classification] a nonparametric prediction method for models with multiple functional and categorical covariates is introduced. The dependent variable can be categorical (binary or multi-class) or continuous, so that both classification and regression problems are considered. In the paper at hand the asymptotic properties of this method are studied. A uniform convergence rate for the regression / classification estimator is given. It is further shown that a data-driven least squares cross-validation method can asymptotically remove irrelevant noise variables automatically.