An Improvement on Vajda’s Inequality

Progress in Probability

Volumn 60, Issue , 2008, Pages 299-304

  Gilardoni, Gustavo L ^a  

^a UNIVERSITY OF BRASILIA   (Brazil)

Author keywords

Information inequalities; Information or Kullback Leibler divergence; relative entropy; symmetric f divergences; variational or L 1 distance

Indexed keywords

EID: 77958612553     PISSN: 10506977     EISSN: 22970428     Source Type: Book Series    
DOI: 10.1007/978-3-7643-8786-0_14     Document Type: Chapter

References (15)

1. I. Csiszár, “A note on Jensen’s inequality,” Studia Sci. Math. Hungar., vol. 1, pp. 185–188, 1966.
2. J.H.B. Kemperman, “On the optimal rate of transmitting information,” Ann. Math. Statist, vol. 40, pp. 2156–2177, Dec. 1969.
3. M.S. Pinsker, Information and Information Stability of Random Variables and Processes. A. Feinstein, tr. and ed., San Francisco: Holden-Day, 1964.
4. S. Kullback, “A lower bound for discrimination information in terms of variation,” IEEE Trans. Inf. Theory, vol. IT-13, pp. 126–127, Jan. 1967.
5. S. Kullback, “Correction to”a lower bound for discrimination information in terms of variation”,” IEEE Trans. Inf. Theory, vol. IT-16, p. 652, 1970.
6. I. Vajda, “Note on discrimination information and variation,” IEEE Trans. Inf. Theory, vol. 16, no. 6, 1970.
7. F. Topsoe, “Bounds for entropy and divergence of distributions over a two-element set,” J. Ineq. Pure Appl. Math., vol. 2, Article 25, 2001.
8. A. Fedotov, P. Harremöes, and F. Topsoe, “Refinements of Pinsker’s Inequality,” IEEE Trans. Inf. Theory, vol. 49, pp. 1491–1498, June 2003.
9. A. Fedotov, P. Harremöes, and F. Topsoe, “Best Pinsker Bound equals Taylor Polynomial of Degree 49,” Computational Technologies, vol. 8, pp. 3–14, 2003.
10. I. Csiszár, “Information-type measures of difference of probability distributions and indirect observations,” Studia Sci. Math. Hungar., vol. 2, pp. 299–318, 1967.
11. S.M. Ali and S.D. Silvey, “A general class of coefficients of divergence of one distribution from another,” J. Roy. Statist. Soc. Ser B, vol. 28, pp. 131–142, 1966.
12. G.L. Gilardoni, “On the minimum f-divergence for given total variation,” C. R. Acad. Sci. Paris, Ser. I, vol. 343, pp. 763–766, 2006.
13. L. LeCam, Asymptotic Methods in Statistical Theory. New York: Springer-Verlag, 1986.
14. S.S. Dragomir, V. Gluščević, and C.E.M. Pearce, “Csisz´ar f-divergence, Ostrowski’s inequality and mutual information,” Nonlinear Analysis, vol. 47, pp. 2375–2386, 2001.
15. F. Topsoe, “Some inequalities for information divergence and related measures of discrimination,” IEEE Trans. Inf. Theory, vol. 46, pp. 1602–1609, 2000.