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

Leonie Selk

Journal of Nonparametric Statistics, 2024, vol. 36, issue 1, 264-286

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.

Date: 2024
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DOI: 10.1080/10485252.2023.2207673

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