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

TL;DR

This paper develops the asymptotic properties of a nonparametric prediction method for models with functional and categorical covariates, demonstrating uniform convergence rates and the ability of cross-validation to automatically select relevant variables.

Contribution

It provides the first asymptotic analysis of a nonparametric method handling multiple functional and categorical covariates, including variable selection.

Findings

Establishes uniform convergence rates for the estimator.

Shows cross-validation can automatically exclude irrelevant variables.

Applicable to both classification and regression problems.

Abstract

In Selk and Gertheiss (2022) 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, thus both classification and regression problems are considered. In the paper at hand the asymptotic properties of this method are developed. A uniform rate of convergence for the regression / classification estimator is given. Further it is shown that, asymptotically, a data-driven least squares cross-validation method can automatically remove irrelevant, noise variables.