Probability Theory and Related Fields

, Volume 79, Issue 3, pp 431–450

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

  • P. Massart

DOI: 10.1007/BF00342234

Cite this article as:
Massart, P. Probab. Th. Rel. Fields (1988) 79: 431. doi:10.1007/BF00342234


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.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • P. Massart
    • 1
  1. 1.U.A. CNRS 743 “Statistique appliquée” MathématiquesUniversité de Paris-SudOrsay CedexFrance