Lower bound on the error probability for families with bounded likelihood ratios
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- by Andrew L. Rukhin PDF
- Proc. Amer. Math. Soc. 119 (1993), 1307-1314 Request permission
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
- Richard Bellman, Introduction to matrix analysis, 2nd ed., McGraw-Hill Book Co., New York-Düsseldorf-London, 1970 (Russian). MR 0258847
- Moshe Ben-Bassat and Josef Raviv, Rényi’s entropy and the probability of error, IEEE Trans. Inform. Theory IT-24 (1978), no. 3, 324–331. MR 484747, DOI 10.1109/tit.1978.1055890
- Abraham Berman and Robert J. Plemmons, Nonnegative matrices in the mathematical sciences, Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 544666
- J. T. Chu and J. D. Chueh, Inequalities between information measures and error probability, J. Franklin Inst. 282 (1966), 121–125. MR 199043, DOI 10.1016/0016-0032(66)90359-0
- Thomas M. Cover, Michael A. Freedman, and Martin E. Hellman, Optimal finite memory learning algorithms for the finite sample problem, Information and Control 30 (1976), no. 1, 49–85. MR 405927 R. G. Gallager, Information theory and reliable communication, Wiley, New York, 1968.
- Martin E. Hellman and Thomas M. Cover, Learning with finite memory, Ann. Math. Statist. 41 (1970), 765–782. MR 272100, DOI 10.1214/aoms/1177696958
- A. Rényi, On some problems of statistics from the point of view of information theory, Proc. Colloquium on Information Theory (Debrecen, 1967) János Bolyai Math. Soc., Budapest, 1968, pp. 343–357. MR 0246424 I. Vajda, Theory of statistical inference and information, Kluwer, Dordrecht, 1989.
Additional Information
- © Copyright 1993 American Mathematical Society
- 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