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Local likelihood density estimation on random fields


Author Info

  • Lee, Y. K.
  • Choi, H.
  • Park, B. U.
  • Yu, K. S.
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    Local likelihood methods hold considerable promise in density estimation. They offer unmatched flexibility and adaptivity as the resulting density estimators inherit both of the best properties of nonparametric approaches and parametric inference. However, the adoption of local likelihood methods with dependent observations, in particular with random fields, is inhibited by lack of knowledge about their properties in the case. In the present paper we detail asymptotic properties of the local likelihood density estimators for stationary random fields in the usual smoothing context of the bandwidth, h, tending to zero as the sample size tends to infinity. The asymptotic analysis is substantially more complex than in ordinary kernel density estimation on random fields.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 68 (2004)
    Issue (Month): 4 (July)
    Pages: 347-357

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    Handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:347-357

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    Keywords: Kernel smoothing Locally parametric density estimation Random fields Strong mixing Small bandwidth asymptotics;


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    1. Biau, GĂ©rard, 2002. "Optimal asymptotic quadratic errors of density estimators on random fields," Statistics & Probability Letters, Elsevier, vol. 60(3), pages 297-307, December.
    2. Tran, L. T. & Yakowitz, S., 1993. "Nearest Neighbor Estimators for Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 23-46, January.
    3. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    4. Carbon, Michel & Tran, Lanh Tat & Wu, Berlin, 1997. "Kernel density estimation for random fields (density estimation for random fields)," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 115-125, December.
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    Cited by:
    1. Mohsen Arefi & Reinhard Viertl & S. Taheri, 2012. "Fuzzy density estimation," Metrika, Springer, vol. 75(1), pages 5-22, January.
    2. Jia Chen & Li-Xin Zhang, 2010. "Local linear M-estimation for spatial processes in fixed-design models," Metrika, Springer, vol. 71(3), pages 319-340, May.


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