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A Note on Asymptotic Normality of Kernel Estimation for Linear Random Fields on Z 2

Author

Listed:
  • Tsung-Lin Cheng

    (National Changhua University of Education)

  • Hwai-Chung Ho

    (National Taiwan University)

  • Xuewen Lu

    (University of Calgary)

Abstract

This note considers the kernel estimation of a linear random field on Z 2. Instead of imposing certain mixing conditions on the random fields, it is assumed that the weights of the innovations satisfy a summability property. By building a martingale decomposition based on a suitable filtration, asymptotic normality is proven for the kernel estimator of the marginal density of the random field.

Suggested Citation

  • Tsung-Lin Cheng & Hwai-Chung Ho & Xuewen Lu, 2008. "A Note on Asymptotic Normality of Kernel Estimation for Linear Random Fields on Z 2," Journal of Theoretical Probability, Springer, vol. 21(2), pages 267-286, June.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:2:d:10.1007_s10959-008-0146-x
    DOI: 10.1007/s10959-008-0146-x
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    References listed on IDEAS

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    1. Tran, L. T. & Yakowitz, S., 1993. "Nearest Neighbor Estimators for Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 23-46, January.
    2. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    3. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
    4. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
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