Uniform consistency in number of neighbors of the kNN estimator of the conditional quantile model
Abstract
We are interested in the efficiency of the nonparametric estimation of the conditional
quantile when the response variable is a scalar given a functional covariate. To do this,
we adopt a technique which is based on the use of the k-Nearest Neighbors procedure
to build a kernel estimator of this model. Then, we establish the uniform conver-
gence in number of neighbors of the constructed estimator. Moreover, we discuss the
optimal choices of different parameters that are involved in the model as well as the
impacts of the obtained results. Finally, we show the applicability and efficiency of
our methodology to investigate the fuel quality by using a Near-infrared spectroscopy
dataset.