Abstract The aim of this paper is to nonparametrically estimate the expectile regression in the case of a functional predictor and a scalar response. More precisely, we construct a kernel-type estimator of the expectile regression function. The main contribution of this study is the establishment of the asymptotic properties of the expectile regression estimator. Precisely, we establish the almost complete convergence with rate. Furthermore, we obtain the asymptotic normality of the proposed estimator under some mild conditions. We provide how to apply our results to construct the confidence intervals. The case of functional predictor is of particular interest and challenge, both from theoretical as well as practical point of view. We discuss the potential impacts of functional expectile regression in NFDA with a particular focus on the supervised classification, prediction and financial risk analysis problems. Finally, the finite-sample performances of the model and the estimation method are illustrated using the analysis of simulated data and real data coming from the financial risk analysis.

中文翻译：

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函数数据核型期望回归估计量的一致性和渐近正态性

摘要 本文的目的是在函数预测器和标量响应的情况下非参数地估计期望回归。更准确地说，我们构建了一个期望回归函数的核型估计器。本研究的主要贡献是建立了期望回归估计量的渐近性质。准确地说，我们建立了几乎完全收敛的速率。此外，我们在一些温和的条件下获得了所提出的估计量的渐近正态性。我们提供了如何应用我们的结果来构建置信区间。从理论和实践的角度来看，函数预测器的案例都特别令人感兴趣和挑战。我们讨论了 NFDA 中功能期望回归的潜在影响，特别关注监督分类、预测和财务风险分析问题。最后，通过对金融风险分析的模拟数据和真实数据的分析，说明了模型和估计方法的有限样本性能。