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.

翻译：Selk与Gertheiss（2022）提出了一种适用于含多个函数型与分类型协变量模型的非参数预测方法。因变量可为分类型（二分类或多分类）或连续型，因此同时涵盖分类与回归问题。本文研究了该方法的渐近性质，给出了回归/分类估计量的一致收敛速率。进一步证明，在渐近意义上，基于数据的最小二乘交叉验证方法能够自动剔除无关噪声变量。