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

Naâmane Laïb and Djamal Louani

Statistics & Probability Letters, 2019, vol. 145, issue C, 187-196

Abstract: 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 σ-fields. A numerical study is performed to illustrate the impact of processes sampling.

Keywords: Asymptotic normality; Confidence bands; Continuous time; Dependent data; Kernel estimator; Sampling (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2018.09.011

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