ABSTRACT We aim to estimate effectively the conditional distribution function (CDF) of a scalar response variable, with missing data at random, given a functional co-variable. For this aim, we combine the local linear approach with the kernel nearest neighbours procedure to construct a new estimator of the CDF. A fundamental issue of interest is to study the impact of the missing observations on the performances of estimators. We establish, under less restrictive conditions, the strong consistency of the constructed estimator. Then, we test first its effectiveness on simulated and real datasets, and then we conclude by a comparison study with classical estimators of the CDF.

中文翻译：

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FDA：当存在缺失数据时，基于条件分布的 kNN 平滑的局部线性估计的理论和实践效率

摘要 我们的目标是有效地估计标量响应变量的条件分布函数 (CDF)，在给定函数协变量的情况下，随机丢失数据。为此，我们将局部线性方法与内核最近邻过程相结合，以构建新的 CDF 估计量。一个有趣的基本问题是研究缺失观测值对估计器性能的影响。我们在限制较少的条件下建立了构造估计量的强一致性。然后，我们首先在模拟数据集和真实数据集上测试其有效性，然后通过与 CDF 的经典估计器进行比较研究得出结论。