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

Publication date: Available online 1 October 2018Source: Statistics & Probability LettersAuthor(s): Naâmane Laïb, Djamal LouaniAbstractOur 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 σ-fields. A numerical study is performed to illustrate the impact of processes sampling.

Source: Statistics and Probability Letters - October 4, 2018 Category: Statistics Source Type: research