A new lower bound for multiple hypothesis testing

IEEE Transactions on Information Theory

Volumn 51, Issue 4, 2005, Pages 1611-1615

  Birgé, Lucien ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Fano's lemma; Minimax risk; Multiple hypothesis testing

Indexed keywords

CODING ERRORS; CONVERGENCE OF NUMERICAL METHODS; DECODING; PARAMETER ESTIMATION; PROBABILITY DISTRIBUTIONS; THEOREM PROVING;

FANO'S LEMMA; LOWER BOUND; MINIMAX RISK; MULTIPLE HYPOTHESIS TESTING;

COMMUNICATION CHANNELS (INFORMATION THEORY);

EID: 17644420339     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2005.844101     Document Type: Article

References (21)

1. B. Yu, "Assouad, Fano and Le Cam," in Festschrift for Lucien Le Cam: Research Papers in Probability and Statistics, D. Pollard, E. Torgersen, and G. Yang, Eds. New York: Springer-Verlag, 1997, pp. 423-435.
2. Y. Yang and A. Barron, "Information-theoretic determination of minimax rates of convergence," Ann. Statist., vol. 27, pp. 1564-1599, 1999.
3. R. M. Fano, "Class notes for transmission of information," MIT, Cambridge, MA, Course 6.574, 1952.
4. R. G. Gallager, Information Theory and Reliable Communication. New York: Wiley, 1968.
5. T.M. Cover and J. A. Thomas, Information Theory. New York: Wiley, 1991.
6. I. A. Ibragimov and R. Z. Has'minskii, Statistical Estimation: Asymptotic Theory. New York: Springer-Verlag, 1981.
7. I. A. Ibragimov and R. Z. Has'minskii "A problem of statistical estimation in Gaussian white noise," in Dokl. Akad. Nauk SSSR, vol. 236, 1977, pp. 1053-1055.
8. I. A. Ibragimov and R. Z. Has'minskii "On estimate of the density function," in Zap. Nauchn. Semin. LOMI, vol. 98, 1980, pp. 61-85.
9. R. Z. Has'minskii, "A lower bound on the risk of nonparametric estimates of densities in the uniform metric," Theory Probab. Appl. vol. 23, pp. 794-798, 1978.
10. L. Birgé, "Approximation dans les espaces métriques et théorie de l'estimation," Z. Wahrscheinlichkeitstheorie Verw. Geb., vol. 65, pp. 181-237, 1983.
11. L. Birgé, "On estimating a density using Hellinger di stance and some other strange facts," Probab. Theory Relat. Fields, vol. 71, pp. 271-291, 1986.
12. A. S. Nemirovski, "Topics in nonparametric statistics," in Lecture on Probability Theory and Statistics, École d'Été de Probabilités de Saint-Flour XXVIII - 1998. Berlin, Germany: Springer-Verlag, 2000, vol. 1738, Lecture Notes in Mathematics.
13. A. Wald, "Sequential tests of statistical hypotheses," Ann. Math. Statist., vol. 16, pp. 117-186, 1945.
14. G. Simons, "Lower bounds for average sample number of sequential multihypothesis tests," Ann. Math. Statist., vol. 38, pp. 1343-1364, 1967.
15. C.E. Shannon, R. G. Gallager, and E. R. Berlekamp, "Lower bounds to error probability for codes on discrete memoryless channels," Inf. Contr., pt. I, vol. 10, pp. 65-103, 1967.
16. A.B. Tsybakov, "Pointwise and sup-norm sharp adaptive estimation of functions on Sobolev classes," Ann. Statist., vol. 26, pp. 2420-2469, 1998.
17. L. Birgé. (2001) A New Look at an Old Result: Fano's Lemma. Lab. de Probabilités de l'Université Paris VI, Paris. Online. Available: http://www.proba.jussieu.fr/mathdoc/preprintshndex.html#2001
18. A.A. Guschin, "On Fano's lemma and similar inequalities for the minimax risk," Math. Methods of Statist., vol. 40, pp. 1247-1251, 2002.
19. L. Birgé and P. Massart, "Minimum contrast estimators on sieves: Exponential bounds and rates of convergence," Bernoulli, vol. 4, pp. 329-375, 1998.
20. A. Wald, Sequential Analysis. New York: Wiley, 1947.
21. T.S. Han and S. Verdú, "Generalizing the Fano inequality," IEEE Trans. Inf. Theory, vol. 40, no. 4, pp. 1247-1251, Ju. 1994.