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On choosing and bounding probability metrics. (English) Zbl 1217.62014
Summary: 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.

MSC:
62E10 Characterization and structure theory of statistical distributions
60B10 Convergence of probability measures
62E99 Statistical distribution theory
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