Transcription of Chapter 3 Total variation distance between measures
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Chapter 3 Total variation distance between measures
Chapter 3 Total variation distance betweenmeasures1. Why bother with different distances?When we work with a family of probability measures ,{P : }, indexedby a metric space , there would seem to be an obvious way to calculatethe distance between measures : use the metric on . For many problems ofestimation, the obvious is what we want. We ask how close (in the metric)we can come to guessing 0, based on an observation fromP 0; we compareestimators based on rates of convergence, or based on expected values of lossfunctions involving the distance from the parametrization is reasonable (whatever that means), distancesmeasured by the metric are reasonable.
2 Chapter 3: Total variation distance between measures total variation distance has properties that will be familiar to students of the Neyman-Pearson approach to hypothesis testing. The Hellinger distance is closely related to the total variation distance—for example, both distances define
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