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Asymptotics of kernel density estimators on weakly associated random fields

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  • Chen, Jia

Abstract

Let ZN, N>=1 denote the integer lattice points in the N-dimensional Euclidean space and be an Rd-valued, strictly stationary, weakly associated random field indexed by ZN. Under mild conditions, as in [Roussas, G.G., 2000. Asymptotic normality of the kernel estimate of a probability density function under association. Statist. Probab. Lett. 50, 1-12], asymptotic normality of the kernel estimator of the multivariate density is established. We also investigate the mean squared error of the estimator towards the unknown density.

Suggested Citation

  • Chen, Jia, 2008. "Asymptotics of kernel density estimators on weakly associated random fields," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3230-3237, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3230-3237
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    References listed on IDEAS

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    1. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    2. Cai, Zongwu & Ould-Saïd, Elias, 2003. "Local M-estimator for nonparametric time series," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 433-449, December.
    3. Roussas, George G., 2000. "Asymptotic normality of the kernel estimate of a probability density function under association," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 1-12, October.
    4. Masry, Elias, 2003. "Local polynomial fitting under association," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 330-359, August.
    5. Burton, Robert M. & Dabrowski, AndréRobert & Dehling, Herold, 1986. "An invariance principle for weakly associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 301-306, December.
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    Cited by:

    1. Hwang, Eunju & Shin, Dong Wan, 2012. "Stationary bootstrap for kernel density estimators under ψ-weak dependence," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1581-1593.

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