Asymptotic normality of kernel density function estimator from continuous time stationary and dependent processes

摘要

Our purpose in this work is to establish the asymptotic normality for the kernel density function estimator in the setting of continuous time stationary and dependent data. Our results allow to construct confidence bands for the density f (x). The proof techniques use martingale difference devices and a sequence of projections on appropriate sigma -fields. A numerical study is performed to illustrate the impact of processes sampling. (C) 2018 Elsevier B.V. All rights reserved.