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Asymptotics for Statistical Distances Based on Voronoi Tessellations

Author

Listed:
  • R. Jiménez

    (CESMa, Universidad Simón Bolívar)

  • J. E. Yukich

    (Lehigh University)

Abstract

We obtain an information-type inequality and a strong law for a wide class of statistical distances between empirical estimates and random measures based on Voronoi tessellations. This extends some basic results in the asymptotic theory of sample spacings, when the cells of the Voronoi tessellation are interpreted as d-dimensional spacings.

Suggested Citation

  • R. Jiménez & J. E. Yukich, 2002. "Asymptotics for Statistical Distances Based on Voronoi Tessellations," Journal of Theoretical Probability, Springer, vol. 15(2), pages 503-541, April.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:2:d:10.1023_a:1014819112010
    DOI: 10.1023/A:1014819112010
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    References listed on IDEAS

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    1. McGivney, K. & Yukich, J. E., 1999. "Asymptotics for Voronoi tessellations on random samples," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 273-288, October.
    2. Yongzhao Shao & Marjorie Hahn, 1999. "Strong Consistency of the Maximum Product of Spacings Estimates with Applications in Nonparametrics and in Estimation of Unimodal Densities," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 31-49, March.
    3. Alfredo N. Iusem & B. F. Svaiter & Marc Teboulle, 1994. "Entropy-Like Proximal Methods in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 790-814, November.
    4. Shao, Yongzhao & Hahn, Marjorie G., 1995. "Limit theorems for the logarithm of sample spacings," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 121-132, August.
    5. Menéndez, M. L. & Morales, D. & Pardo, L. & Zografos, K., 1999. "Statistical inference for finite Markov chains based on divergences," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 9-17, January.
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