On choosing and bounding probability metrics

2002/09/03 by Alison L. Gibbs, Francis Edward Su · 10 citations
Mathematics · #math.PR #msc:60B10

paper · pdf

published as International Statistical Review (2002), vol. 70, number 3, 419-435. · To appear, International Statistical Review. Related work at http://www.math.hmc.edu/~su/papers.html

arxiv created 2002/09/03 · arxiv updated 2009/11/30

Abstract

When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by statisticians and probabilists. We focus on these metrics because they are either well-known, commonly used, or admit practical bounding techniques. We summarize these relationships in a handy reference diagram, and also give examples to show how rates of convergence can depend on the metric chosen.

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