ABSTRACT This paper develops a new automatic and location-adaptive procedure for estimating regression in a Functional Single-Index Model (FSIM). This procedure is based on k-Nearest Neighbours (kNN) ideas. The asymptotic study includes results for automatically data-driven selected number of neighbours, making the procedure directly usable in practice. The local feature of the kNN approach insures higher predictive power compared with usual kernel estimates, as illustrated in some finite sample analysis. As by-product, we state as preliminary tools some new uniform asymptotic results for kernel estimates in the FSIM model.

中文翻译：

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函数单指标回归中的自动和位置自适应估计

摘要 本文开发了一种新的自动和位置自适应程序，用于估计功能单指数模型 (FSIM) 中的回归。此过程基于 k-最近邻 (kNN) 思想。渐近研究包括自动数据驱动选定数量的邻居的结果，使该过程可直接用于实践。与通常的核估计相比，kNN 方法的局部特征确保了更高的预测能力，如某些有限样本分析所示。作为副产品，我们将 FSIM 模型中核估计的一些新的统一渐近结果作为初步工具声明。