Asymptotic Confidence Bands for Density and Regression Functions in the Gaussian Case

Abstract

In this paper, we obtain asymptotic confidence bands for both the density and regression functions in the framework of nonparametric estimation. Beforehand, the asymptotic behaviors in probability of the kernel estimator of the density and the Nadaraya-Watson estimator of the regression function are described while local and global optimal smoothing parameters are investigated. A simulation study is conducted, showing the good performance of the confidence bands obtained for small sample.