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.

翻译：本文旨在处理预测变量由函数型变量与高维向量混合构成时回归问题的降维问题。我们提出了一种融合稀疏线性思想与半参数方法的灵活模型。文章提供了广泛的渐近理论结果：涵盖估计量的收敛速率以及变量选择过程的渐近性质。通过有限样本模拟实验分析了实际应用问题，并在Tecator数据上的应用实例验证了所提方法的有效性。