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Asymptotic normality of recursive density estimates under some dependence assumptions

Author

Listed:
  • Han-Ying Liang
  • Jong-Il Baek

Abstract

Let {X n ,n≥1} be a strictly stationary sequence of negatively associated random variables with the marginal probability density function f(x), the recursive kernel estimate of f(x) is defined by [InlineMediaObject not available: see fulltext.] where h n is a sequence of positive bandwidths tending to 0, as n→∞, K(·) is a univariate kernel function. In this note, we discuss the point asymptotic normality for f n (x). Copyright Springer-Verlag 2004

Suggested Citation

  • Han-Ying Liang & Jong-Il Baek, 2004. "Asymptotic normality of recursive density estimates under some dependence assumptions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 155-166, September.
    • Handle: RePEc:spr:metrik:v:60:y:2004:i:2:p:155-166
    DOI: 10.1007/s001840300302
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    Cited by:

    1. P. Cattiaux & José R. León & C. Prieur, 2015. "Recursive estimation for stochastic damping hamiltonian systems," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 401-424, September.
    2. Amiri, Aboubacar & Dabo-Niang, Sophie, 2018. "Density estimation over spatio-temporal data streams," Econometrics and Statistics, Elsevier, vol. 5(C), pages 148-170.
    3. Wu, Yi & Yu, Wei & Wang, Xuejun & Shen, Aiting, 2021. "The rate of complete consistency for recursive probability density estimator under strong mixing samples," Statistics & Probability Letters, Elsevier, vol. 176(C).
    4. Han-Ying Liang & Jong-Il Baek, 2008. "Berry–Esseen bounds for density estimates under NA assumption," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 305-322, November.

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