Journal
INTERNATIONAL STATISTICAL REVIEW
Volume 70, Issue 3, Pages 419-435Publisher
WILEY
DOI: 10.2307/1403865
Keywords
discrepancy; hellinger distance; probability metrics; prokhorov metric; relative entropy; rates of convergence; wasserstein distance
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When studying convergence of measures, an. important, issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a means of deriving bounds for another one in an applied problem. Considering other metrics can also provide alternate insights. We also give examples that show that rates of convergence can strongly depend on the metric chosen. Careful consideration is necessary when choosing a metric.
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