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Optimal asymptotic quadratic errors of density estimators on random fields

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  • Biau, Gérard

Abstract

Let denote the integer lattice points in the N-dimensional Euclidean space. Kernel estimation of the multivariate density of a random field indexed by is investigated. The loss between the estimator and the unknown density is measured by means of mean squared and mean integrated squared errors. Under mild mixing conditions, we show that the kernel density estimator has exactly the same asymptotic error as in the i.i.d. case.

Suggested Citation

  • Biau, Gérard, 2002. "Optimal asymptotic quadratic errors of density estimators on random fields," Statistics & Probability Letters, Elsevier, vol. 60(3), pages 297-307, December.
    • Handle: RePEc:eee:stapro:v:60:y:2002:i:3:p:297-307
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    References listed on IDEAS

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    1. 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.
    2. Bosq, Denis, 1995. "Optimal asymptotic quadratic error of density estimators for strong mixing or chaotic data," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 339-347, March.
    3. Marc Hallin & Michel Carbon & Lanh T. Tran, 1996. "Kernel density estimation on random fields: the L1 theory," ULB Institutional Repository 2013/2065, ULB -- Universite Libre de Bruxelles.
    4. Tran, L. T. & Yakowitz, S., 1993. "Nearest Neighbor Estimators for Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 23-46, January.
    5. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
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    Cited by:

    1. Younso, Ahmad, 2017. "On the consistency of a new kernel rule for spatially dependent data," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 64-71.
    2. Michel Harel & Jean-François Lenain & Joseph Ngatchou-Wandji, 2016. "Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 296-321, June.
    3. Ahmad Younso, 2023. "On the consistency of mode estimate for spatially dependent data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(3), pages 343-372, April.
    4. Lee, Y. K. & Choi, H. & Park, B. U. & Yu, K. S., 2004. "Local likelihood density estimation on random fields," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 347-357, July.
    5. Livasoa Andriamampionona & Victor Harison & Michel Harel, 2024. "Non-Parametric Estimation of the Renewal Function for Multidimensional Random Fields," Mathematics, MDPI, vol. 12(12), pages 1-22, June.
    6. Gérard Biau & Benoît Cadre, 2004. "Nonparametric Spatial Prediction," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 327-349, October.

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