| Title:
|
Blended $\phi$-divergences with examples (English) |
| Author:
|
Kůs, Václav |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
[43]-54 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Several new examples of divergences emerged in the recent literature called blended divergences. Mostly these examples are constructed by the modification or parametrization of the old well-known phi-divergences. Newly introduced parameter is often called blending parameter. In this paper we present compact theory of blended divergences which provides us with a generally applicable method for finding new classes of divergences containing any two divergences $D_0$ and $D_1$ given in advance. Several examples of blends of well-known divergences are given. (English) |
| Keyword:
|
divergences of probability distributions |
| Keyword:
|
blended divergences |
| Keyword:
|
statistical applications |
| MSC:
|
62B10 |
| MSC:
|
62F35 |
| MSC:
|
62F99 |
| MSC:
|
62G35 |
| MSC:
|
62G99 |
| idZBL:
|
Zbl 1243.62004 |
| idMR:
|
MR1980123 |
| . |
| Date available:
|
2009-09-24T19:51:02Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135507 |
| . |
| Reference:
|
[1] Cressie N., Read T. R. C.: Multinomial goodness-of-fit tests.J. Roy. Statist. Soc. Ser. A 46 (1984), 440–464 Zbl 0571.62017, MR 0790631 |
| Reference:
|
[2] Kafka P., Österreicher F., Vincze I.: On powers of $f$-divergences defining a distance.Studia Sci. Math. Hungar. 26 (1991), 415–422 MR 1197090 |
| Reference:
|
[3] Kůs V.: Divergences and Generalized Score Functions in Statistical Inference.Ph.D. Thesis, Czech Technical University, Prague 1998 |
| Reference:
|
[4] Cam L. Le: Asymptotic Methods in Statistical Decision Theory.Springer, New York 1986 Zbl 0605.62002, MR 0856411 |
| Reference:
|
[5] Lindsay B. G.: Efficiency versus robustness.The case for minimum Hellinger distance and other methods. Ann. Statist. 22 (1994), 1081–1114 Zbl 0807.62030, MR 1292557, 10.1214/aos/1176325512 |
| Reference:
|
[6] Menéndez M., Morales D., Pardo, L., Vajda I.: Two approaches to grouping of data and related disparity statistics.Comm. Statist. A – Theory Methods 27 (1998), 609–633 Zbl 1126.62300, MR 1619038, 10.1080/03610929808832117 |
| Reference:
|
[7] Österreicher. F.: On a class of perimeter-type distances of probability distributions.Kybernetika 32 (1996), 389–393 Zbl 0897.60015, MR 1420130 |
| Reference:
|
[8] Park, Ch., Basu A., Basu S.: Robust minimum distance inference based on combined distances.Comm. Statist. B – Simulation Comput. 24 (1995), 653–673 Zbl 0850.62243, 10.1080/03610919508813265 |
| Reference:
|
[9] Read R. C., Cressie N. A. C.: Goodness-of-fit Statistics for Discrete Multivariate Data.Springer, Berlin 1988 Zbl 0663.62065, MR 0955054 |
| Reference:
|
[10] Vajda I.: Theory of Statistical Inference and Information.Kluwer, Boston 1989 Zbl 0711.62002 |
| Reference:
|
[11] Vajda I.: Information–Theoretic Methods in Statistics.Research Report No. 1834, ÚTIA, Academy of Sciences of the Czech Republic, Prague 1995 |
| . |
