Abstract

We consider the problem of nonparametric estimation of certain conditional models when the explanatory variable is functional. The models studied are the Conditional Expectation (CE), the Conditional Distribution Function (CDF) and the Conditional Probability Density (CPD). The estimators are constructed by combining the local linear method and the k-Nearest Neighbors (kNN) smoothing approach. For each of the three models, we define an optimal estimator associated with the best number of neighbors chosen using two bandwidth selection procedures which are the cross-validation criterion and the bootstrap smoothing rule. The asymptotic properties of these optimal kNN Local Linear Estimators (k$k$$k$ NN- LLE) are established under some standard conditions. The performances of the finite samples of these estimators are then examined and compared through a Monte-carlo study. In addition, an application on the riboflavin content in the yogurt using the Near-infrared curves is carried out to demonstrate the usefulness of the models proposed in the point-wise prediction as well as for the predictive interval.

摘要

当解释变量是函数时，我们考虑某些条件模型的非参数估计问题。研究的模型是条件期望（CE）、条件分布函数（CDF）和条件概率密度（CPD）。估计量是通过结合局部线性方法和k最近邻 ( k NN) 平滑方法构建的。对于这三个模型中的每一个，我们定义了一个与使用两个带宽选择程序（交叉验证标准和引导平滑规则）选择的最佳邻居数量相关的最佳估计器。这些最优k 个NN 局部线性估计器的渐近性质(k$k$$k$NN- LLE）是在某些标准条件下建立的。然后通过蒙特卡洛研究检查和比较这些估计器的有限样本的性能。此外，还使用近红外曲线对酸奶中的核黄素含量进行了应用，以证明所提出的模型在逐点预测以及预测区间中的有用性。