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:在Selk和Gertheiss(2022年)中,引入了一种多功能和分类协变量模型的非参数预测方法。该因变量可以是分类(二元或多类)或连续变量,因此考虑了分类和回归问题。本文开展了该方法的渐近特性。为回归/分类估计器提供了一种均匀收敛速率。此外,还证明了,渐近时,基于数据的最小二乘交叉验证方法可以自动排除无关的噪声变量。