This paper focuses on a semiparametric regression model in which the response variable is explained by the sum of two components. One of them is parametric (linear), the corresponding explanatory variable is measured with additive error and its dimension is finite ($p$). The other component models, in a nonparametric way, the effect of a functional variable (infinite dimension) on the response. $k$-NN based estimators are proposed for each component, and some asymptotic results are obtained. A simulation study illustrates the behaviour of such estimators for finite sample sizes, while an application to real data shows the usefulness of our proposal.

翻译：本文研究一种半参数回归模型，其中响应变量由两个分量之和解释。一个分量为参数型（线性），其对应解释变量存在加性测量误差且维度有限（$p$）。另一分量以非参数方式建模函数型变量（无穷维度）对响应变量的影响。针对各分量提出了基于$k$-NN的估计量，并获得了渐近性质。通过仿真研究展示了这些估计量在有限样本下的表现，同时基于真实数据的应用验证了所提方法的实用性。