Computational aspects of the kNN local linear smoothing for some conditional models in high dimensional statistics

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 ( 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.