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

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  • Laïb, Naâmane
  • Louani, Djamal

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.

Suggested Citation

  • Laïb, Naâmane & Louani, Djamal, 2019. "Asymptotic normality of kernel density function estimator from continuous time stationary and dependent processes," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 187-196.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:187-196
    DOI: 10.1016/j.spl.2018.09.011
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    References listed on IDEAS

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    1. Didi, Sultana & Louani, Djamal, 2013. "Consistency results for the kernel density estimate on continuous time stationary and dependent data," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1262-1270.
    2. Yogendra Chaubey & Naâmane Laïb & Arusharka Sen, 2010. "Generalised kernel smoothing for non-negative stationary ergodic processes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 973-997.
    3. D. Blanke & B. Pumo, 2003. "Optimal sampling for density estimation in continuous time," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 1-23, January.
    4. Laib, Naâmane & Louani, Djamal, 2010. "Nonparametric kernel regression estimation for functional stationary ergodic data: Asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2266-2281, November.
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    Cited by:

    1. Gao, Min & Yang, Wenzhi & Wu, Shipeng & Yu, Wei, 2022. "Asymptotic normality of residual density estimator in stationary and explosive autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    2. Chaouch, Mohamed & Laïb, Naâmane, 2019. "Optimal asymptotic MSE of kernel regression estimate for continuous time processes with missing at random response," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    3. Dawei Lu & Lina Wang, 2021. "On the Rates of Asymptotic Normality for Bernstein Polynomial Estimators in a Triangular Array," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1519-1536, December.

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