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About the prohorov distance between the uniform distribution over the unit cube in R dand its empirical measure
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  • Published: October 1988

About the prohorov distance between the uniform distribution over the unit cube in R dand its empirical measure

  • P. Massart1 

Probability Theory and Related Fields volume 79, pages 431–450 (1988)Cite this article

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Summary

We compute the almost sure order of convergence of the Prokhorov distance between the uniform distribution P over [0, 1]d and the empirical measure associated with n independent observations with (common) distribution P. We show that this order of convergence is n -1/d up to a power of log(n). This result extends to the case where the observations are weakly dependent.

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Authors and Affiliations

  1. U.A. CNRS 743 “Statistique appliquée” Mathématiques, Université de Paris-Sud, Bât. 425, F-91405, Orsay Cedex, France

    P. Massart

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  1. P. Massart
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Massart, P. About the prohorov distance between the uniform distribution over the unit cube in R dand its empirical measure. Probab. Th. Rel. Fields 79, 431–450 (1988). https://doi.org/10.1007/BF00342234

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  • Received: 26 June 1986

  • Revised: 07 April 1988

  • Issue Date: October 1988

  • DOI: https://doi.org/10.1007/BF00342234

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Keywords

  • Uniform Distribution
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Unit Cube
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