 ## The Minimum Increment of f-Divergences Given Total Variation Distancesстатья Информация о цитировании статьи получена из Scopus
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Дата последнего поиска статьи во внешних источниках: 3 мая 2017 г.
• Автор:
• Журнал: Mathematical Methods of Statistics
• Том: 25
• Номер: 4
• Год издания: 2016
• Первая страница: 304
• Последняя страница: 312
• DOI: 10.3103/S1066530716040049
• Аннотация: Let (Pi,Qi), i = 0, 1, be two pairs of probability measures defined on measurable spaces (Ωi,Fi) respectively. Assume that the pair (P1,Q1) is more informative than (P0,Q0) for testing problems. This amounts to say that If (P1,Q1) ≥ If (P0,Q0), where If (·, ·) is an arbitrary fdivergence. We find a precise lower bound for the increment of f-divergences If (P1,Q1) − If (P0,Q0) provided that the total variation distances Q1 − P1 and Q0 − P0 are given. This optimization problem can be reduced to the case where P1 and Q1 are defined on the space consisting of four points, and P0 and Q0 are obtained from P1 and Q1 respectively by merging two of these four points. The result includes the well-known lower and upper bounds for If (P,Q) given Q − P.
• Добавил в систему: Гущин Александр Александрович

### Работа с статьей

  Gushchin A. A. The minimum increment of f-divergences given total variation distances // Mathematical Methods of Statistics. — 2016. — Vol. 25, no. 4. — P. 304–312. Let (Pi,Qi), i = 0, 1, be two pairs of probability measures defined on measurable spaces (Ωi,Fi) respectively. Assume that the pair (P1,Q1) is more informative than (P0,Q0) for testing problems. This amounts to say that If (P1,Q1) ≥ If (P0,Q0), where If (·, ·) is an arbitrary fdivergence. We find a precise lower bound for the increment of f-divergences If (P1,Q1) − If (P0,Q0) provided that the total variation distances Q1 − P1 and Q0 − P0 are given. This optimization problem can be reduced to the case where P1 and Q1 are defined on the space consisting of four points, and P0 and Q0 are obtained from P1 and Q1 respectively by merging two of these four points. The result includes the well-known lower and upper bounds for If (P,Q) given Q − P. [ DOI ]