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On the Rate of Convergence of Empirical Measures in $\infty$-transportation Distance

  Published:2015-03-02
 Printed: Dec 2015
  • Nicolas Garcia Trillos,
    Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA.
  • Dejan Slepcev,
    Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA.
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Abstract

We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is optimal in terms of scaling with the number of sample points.
Keywords: rate, convergence rate, convergence
MSC Classifications: 01B01 show english descriptions unknown classification 01B01 01B01 - unknown classification 01B01
 

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