Article - preprint
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.
© 2002 John Wiley & Sons
Alison L. Gibbs and Francis Edward Su. On choosing and bounding probability metrics. International Statistical Review, 70(3):419–435, 2002.
Author's pre-print manuscript available for download.
The definitive version is available at http://dx.doi.org/10.1111/j.1751-5823.2002.tb00178.x.