This paper aims to front with dimensionality reduction in regression setting when the predictors are a mixture of functional variable and high-dimensional vector. A flexible model, combining both sparse linear ideas together with semiparametrics, is proposed. A wide scope of asymptotic results is provided: this covers as well rates of convergence of the estimators as asymptotic behaviour of the variable selection procedure. Practical issues are analysed through finite sample-simulated experiments, while an application to Tecator’s data illustrates the usefulness of our methodology.

中文翻译：

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当预测变量是功能变量和高维变量的混合时，稀疏半参数回归

当预测变量是功能变量和高维向量的混合时，本文旨在降低回归设置中的维数。提出了一种将稀疏线性思想与半参数结合在一起的灵活模型。提供了广泛的渐近结果：这涵盖了变量选择过程的渐近行为以及估计量的收敛速度。通过有限的样本模拟实验对实际问题进行了分析，而对Tecator数据的应用说明了我们方法论的有用性。