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Frequency Polygons for Random Fields

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  • Michel Carbon

    (Crest)

Abstract

The purpose of this paper is to investigate the frequency polygon as a densityestimator for stationary random fields indexed by multidimensional lattice pointsspace. Optimal bin widths which asymptotically minimize integrated errors (IMSE)are derived. Under weak conditions, frequency polygons achieve the same rate ofconvergence to zero of the IMSE as kernel estimators. They can also attain theoptimal uniform rate of convergence under general conditions. Frequency polygonsthus appear to be very good density estimators with respect to both criteria of IMSEand uniform convergence.

Suggested Citation

  • Michel Carbon, 2005. "Frequency Polygons for Random Fields," Working Papers 2005-04, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2005-04
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    References listed on IDEAS

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    1. Politis, D. N. & Romano, J. P., 1993. "Nonparametric Resampling for Homogeneous Strong Mixing Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 301-328, November.
    2. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    3. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    4. Masry, Elias & Györfi, László, 1987. "Strong consistency and rates for recursive probability density estimators of stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 79-93, June.
    5. Tran, L. T. & Yakowitz, S., 1993. "Nearest Neighbor Estimators for Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 23-46, January.
    6. 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.
    7. 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.
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