Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Lower bound on the error probability for families with bounded likelihood ratios


Author: Andrew L. Rukhin
Journal: Proc. Amer. Math. Soc. 119 (1993), 1307-1314
MSC: Primary 62C05; Secondary 62F11, 62F15, 62F35
DOI: https://doi.org/10.1090/S0002-9939-1993-1166361-X
MathSciNet review: 1166361
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In the classification problem a new sharp lower bound for the error probability is derived. This bound depends only on the prior probabilities and on the support of pairwise likelihood ratios.


References [Enhancements On Off] (What's this?)

  • [1] R. Bellman, Introduction to matrix analysis, 2nd ed., McGraw-Hill, New York, 1970. MR 0258847 (41:3493)
  • [2] M. Ben-Bassat and J. Raviv, Renyi's entropy and the probability of error, IEEE Trans. Inform. Theory IT-24 (1978), 324-331. MR 0484747 (58:4626)
  • [3] A. Berman and R. J. Plemmons, Nonngative matrices in the mathematical sciences, Academic Press, New York, 1979. MR 544666 (82b:15013)
  • [4] J. T. Chu and J. C. Chueh, Inequalities between information measures and error probability, J. Franklin Inst. 282 (1966), 121-125. MR 0199043 (33:7193)
  • [5] T. M. Cover, M. A. Freedman, and M. E. Hellman, Optimal finite memory learning algorithms for the finite sample problem, Information and Control 30 (1976), 49-85. MR 0405927 (53:9719)
  • [6] R. G. Gallager, Information theory and reliable communication, Wiley, New York, 1968.
  • [7] M. E. Hellman and T. M. Cover, Learning with finite memory, Ann. Math. Statist. 41 (1970), 765-782. MR 0272100 (42:6981)
  • [8] A. Renyi, On some problems of statistics from the point of view of information theory, Proceedings of the Colloquium on Information Theory (Debrecen, 1969), Bolyai Janos Matematikai Tarsulat, Bolyai Math. Soc. MR 0246424 (39:7728)
  • [9] I. Vajda, Theory of statistical inference and information, Kluwer, Dordrecht, 1989.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 62C05, 62F11, 62F15, 62F35

Retrieve articles in all journals with MSC: 62C05, 62F11, 62F15, 62F35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1166361-X
Keywords: Classification problem, error probability, likelihood ratios, linear programming, M-matrix
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society