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On Choosing and Bounding Probability Metrics |
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| Authors: | Alison L Gibbs Francis Edward Su |
| Institution: | Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada, M3J 1P3. E-mail: .;Department of Mathematics, Harvey Mudd College, Claremont, CA, USA 91711. E-mail: |
| Abstract: | 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. |
| Keywords: | Discrepancy Hellinger distance Probability metrics Prokhorov metric Relative entropy Rates of convergence Wasserstein distance |