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Volumn 56, Issue 11, 2010, Pages 5377-5386

On Pinsker's and Vajda's type inequalities for Csiszár's f-divergences

Author keywords

Hellinger discrimination; information inequalities; KullbackLeibler divergence; relative entropy; relative information; Rnyi's information gain; variational or L1distance

Indexed keywords

HELLINGER DISCRIMINATION; INFORMATION GAIN; INFORMATION INEQUALITIES; KULLBACK LEIBLER DIVERGENCE; RELATIVE ENTROPY; RELATIVE INFORMATION; VARIATIONAL OR L1DISTANCE;

EID: 77958532086     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2068710     Document Type: Article
Times cited : (80)

References (49)
  • 1
    • 0000753060 scopus 로고
    • Some limit theorems for random functions - I
    • V. A. Volkonskij and J. A. Rozanov, "Some limit theorems for random functions - I," Theory Prob. Applicat., vol.4, pp. 178-197, 1959.
    • (1959) Theory Prob. Applicat. , vol.4 , pp. 178-197
    • Volkonskij, V.A.1    Rozanov, J.A.2
  • 3
    • 0000061719 scopus 로고
    • Entropy and the central limit theorem
    • A. R. Barron, "Entropy and the central limit theorem," Ann. Probab., vol.14, no.1, pp. 336-342, 1986.
    • (1986) Ann. Probab. , vol.14 , Issue.1 , pp. 336-342
    • Barron, A.R.1
  • 4
    • 0002591570 scopus 로고
    • Information theoretical optimization techniques
    • F. Topsøe, "Information theoretical optimization techniques," Kybernetika, vol.15, no.1, pp. 8-27, 1979.
    • (1979) Kybernetika , vol.15 , Issue.1 , pp. 8-27
    • Topsøe, F.1
  • 5
    • 4544261302 scopus 로고    scopus 로고
    • Rate of convergence to Poisson law in terms of information divergence
    • P. Harremoës and P. Ruzankin, "Rate of convergence to Poisson law in terms of information divergence," IEEE Trans. Inf. Theory, vol.50, no.9, pp. 2145-2149, 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , Issue.9 , pp. 2145-2149
    • Harremoës, P.1    Ruzankin, P.2
  • 6
    • 0036710614 scopus 로고    scopus 로고
    • Best constants for Gagliardo-Niremberg inequalities and applications to nonlinear difussions
    • M. Del Pino and J. Dolbeault, "Best constants for Gagliardo-Niremberg inequalities and applications to nonlinear difussions," J. Math. Pures Appl., vol.81, pp. 847-875, 2002.
    • (2002) J. Math. Pures Appl. , vol.81 , pp. 847-875
    • Del Pino, M.1    Dolbeault, J.2
  • 7
    • 0000489740 scopus 로고
    • Information-type measures of difference of probability distributions and indirect observations
    • I. Csiszár, "Information-type measures of difference of probability distributions and indirect observations," Studia Sci. Math. Hungary, vol.2, pp. 299-318, 1967.
    • (1967) Studia Sci. Math. Hungary , vol.2 , pp. 299-318
    • Csiszár, I.1
  • 8
    • 0001698345 scopus 로고
    • On the optimal rate of transmitting information
    • Dec.
    • J. H. B. Kemperman, "On the optimal rate of transmitting information," Ann. Math. Statist, vol.40, pp. 2156-2177, Dec. 1969.
    • (1969) Ann. Math. Statist , vol.40 , pp. 2156-2177
    • Kemperman, J.H.B.1
  • 10
    • 0001055303 scopus 로고
    • Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas
    • H. P. McKean Jr., "Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas," Arch. Rational Mech. Anal., vol.21, pp. 343-367, 1966.
    • (1966) Arch. Rational Mech. Anal. , vol.21 , pp. 343-367
    • McKean Jr., H.P.1
  • 11
    • 0000864925 scopus 로고
    • A note on Jensen's inequality
    • I. Csiszár, "A note on Jensen's inequality," Studia Sci. Math. Hungary, vol.1, pp. 185-188, 1966.
    • (1966) Studia Sci. Math. Hungary , vol.1 , pp. 185-188
    • Csiszár, I.1
  • 12
    • 84941465845 scopus 로고
    • A lower bound for discrimination information in terms of variation
    • S. Kullback, "A lower bound for discrimination information in terms of variation," IEEE Trans. Inf. Theory, vol.IT-13, pp. 126-127, Jan. 1967.
    • (1967) IEEE Trans. Inf. Theory , vol.IT-13 , pp. 126-127
    • Kullback, S.1
  • 13
    • 0038517228 scopus 로고
    • Correction to " A lower bound for discrimination information in terms of variation","
    • S. Kullback, "Correction to "A lower bound for discrimination information in terms of variation"," IEEE Trans. Inf. Theory, vol.16, p. 652, 1970.
    • (1970) IEEE Trans. Inf. Theory , vol.16 , pp. 652
    • Kullback, S.1
  • 14
    • 0001157377 scopus 로고
    • Note on discrimination information and variation
    • I. Vajda, "Note on discrimination information and variation," IEEE Trans. Inf. Theory, vol.16, no.6, pp. 771-773, 1970.
    • (1970) IEEE Trans. Inf. Theory , vol.16 , Issue.6 , pp. 771-773
    • Vajda, I.1
  • 15
    • 5044250398 scopus 로고    scopus 로고
    • Bounds for entropy and divergence of distributions over a two-element set
    • Article 25
    • F. Topsøe, "Bounds for entropy and divergence of distributions over a two-element set," J. Ineq. Pure Appl. Math., vol. 2, no. Article 25, 2001.
    • (2001) J. Ineq. Pure Appl. Math. , vol.2
    • Topsøe, F.1
  • 16
    • 77958588834 scopus 로고    scopus 로고
    • Best Pinsker bound equals Taylor polynomial of degree 49
    • A. Fedotov, P. Harremoës, and F. Topsøe, "Best Pinsker bound equals Taylor polynomial of degree 49," Comput. Technol., vol.8, no.5, pp. 3-14, 2003.
    • (2003) Comput. Technol. , vol.8 , Issue.5 , pp. 3-14
    • Fedotov, A.1    Harremoës, P.2    Topsøe, F.3
  • 17
    • 0001856347 scopus 로고
    • Eine informationstheoretische Ungleichung und ihre anwendung auf den Beweis der ergodizität von Markoffschen Ketten
    • I. Csiszár, "Eine informationstheoretische Ungleichung und ihre anwendung auf den Beweis der ergodizität von Markoffschen Ketten," Publ. Math. Inst. Hungary Acad., vol.8, pp. 95-108, 1963.
    • (1963) Publ. Math. Inst. Hungary Acad. , vol.8 , pp. 95-108
    • Csiszár, I.1
  • 18
    • 0001199215 scopus 로고
    • A general class of coefficients of divergence of one distribution from another
    • S. M. Ali and S. D. Silvey, "A general class of coefficients of divergence of one distribution from another," J. Roy. Statist. Soc. B, vol.28, pp. 131-142, 1966.
    • (1966) J. Roy. Statist. Soc. B , vol.28 , pp. 131-142
    • Ali, S.M.1    Silvey, S.D.2
  • 19
    • 43649101458 scopus 로고    scopus 로고
    • On generalized entropies, Bayesian decisions and statistical diversity
    • I. Vajda and J. Zvárová, "On generalized entropies, Bayesian decisions and statistical diversity," Kybernetika, vol.43, pp. 675-696, 2007.
    • (2007) Kybernetika , vol.43 , pp. 675-696
    • Vajda, I.1    Zvárová, J.2
  • 20
    • 33947426775 scopus 로고    scopus 로고
    • On divergences and informations in statistics and information theory
    • F. Liese and I.Vajda, "On divergences and informations in statistics and information theory," IEEE Trans. Inf. Theory, vol.52, pp. 4394-4412, 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , pp. 4394-4412
    • Liese, F.1    Vajda, I.2
  • 21
    • 33750344778 scopus 로고    scopus 로고
    • Very accurate posterior approximations based on finite mixtures of the hyperparameters conditionals
    • G. L. Gilardoni, "Very accurate posterior approximations based on finite mixtures of the hyperparameters conditionals," Comput. Statist. Data Anal., vol.51, no.2, pp. 872-884, 2006.
    • (2006) Comput. Statist. Data Anal. , vol.51 , Issue.2 , pp. 872-884
    • Gilardoni, G.L.1
  • 22
    • 13444267746 scopus 로고    scopus 로고
    • Cramér-Rao and moment-entropy inequalities for Renyi entropy and generalized Fisher information
    • D. Y. E. Lutwak and G. Y. Zhang, "Cramér-Rao and moment-entropy inequalities for Renyi entropy and generalized Fisher information," IEEE Trans. Inf. Theory, vol.51, pp. 473-478, 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , pp. 473-478
    • Lutwak, D.Y.E.1    Zhang, G.Y.2
  • 23
    • 8644228595 scopus 로고    scopus 로고
    • Accuracy of posterior approximations via chi-squared and harmonic divergences
    • G. L. Gilardoni, "Accuracy of posterior approximations via chi-squared and harmonic divergences," J. Statist. Planning Inference, vol.128, no.2, pp. 475-487, 2005.
    • (2005) J. Statist. Planning Inference , vol.128 , Issue.2 , pp. 475-487
    • Gilardoni, G.L.1
  • 25
    • 27744602833 scopus 로고    scopus 로고
    • Generalized relative information and information inequalities
    • Article 21
    • I. Taneja, "Generalized relative information and information inequalities," J. Ineq. Pure Appl. Math., vol.5, no.1, Article 21, 2004.
    • (2004) J. Ineq. Pure Appl. Math. , vol.5 , Issue.1
    • Taneja, I.1
  • 26
    • 33646516485 scopus 로고
    • Possible generalization of Boltzmann-Gibbs statistics
    • C. Tsallis, "Possible generalization of Boltzmann-Gibbs statistics," J. Stat. Phys., vol.52, p. 479, 1988.
    • (1988) J. Stat. Phys. , vol.52 , pp. 479
    • Tsallis, C.1
  • 27
    • 0000557977 scopus 로고
    • Multinomial goodness-of-fit tests
    • N. Cressie and T. R. C. Read, "Multinomial goodness-of-fit tests," J. Royal Statist. Soc. B, vol.46, pp. 440-464, 1984.
    • (1984) J. Royal Statist. Soc. B , vol.46 , pp. 440-464
    • Cressie, N.1    Read, T.R.C.2
  • 28
    • 0346361442 scopus 로고    scopus 로고
    • Information and entropy econometrics-Editor's view
    • A. Golan, "Information and entropy econometrics-Editor's view," J. Econometrics, vol.107, pp. 1-15, 2002.
    • (2002) J. Econometrics , vol.107 , pp. 1-15
    • Golan, A.1
  • 29
    • 0032679969 scopus 로고    scopus 로고
    • Some inequalities relating different measures of divergence between two probability distributions
    • L.Withers Jr., "Some inequalities relating different measures of divergence between two probability distributions," IEEE Trans. Inf. Theory, vol.45, no.5, pp. 1728-1735, 1999.
    • (1999) IEEE Trans. Inf. Theory , vol.45 , Issue.5 , pp. 1728-1735
    • Withers Jr., L.1
  • 30
  • 31
    • 0029219702 scopus 로고
    • Generalized cutoff rates and Rényi information measures
    • I. Csiszár, "Generalized cutoff rates and Rényi information measures," IEEE Trans. Inf. Theory, vol.41, pp. 26-34, Jan. 1995.
    • (1995) IEEE Trans. Inf. Theory , vol.41 , pp. 26-34
    • Csiszár, I.1
  • 34
    • 0035420978 scopus 로고    scopus 로고
    • Csiszár divergence, Ostrowski's inequality and mutual information
    • S. S. Dragomir, V. Gluscević, and C. E. M. Pearce, "Csiszár divergence, Ostrowski's inequality and mutual information," Nonlinear Anal., vol.47, pp. 2375-2386, 2001.
    • (2001) Nonlinear Anal. , vol.47 , pp. 2375-2386
    • Dragomir, S.S.1    Gluscević, V.2    Pearce, C.E.M.3
  • 35
    • 0034224418 scopus 로고    scopus 로고
    • Some inequalities for information divergence and related measures of discrimination
    • F. Topsøe, "Some inequalities for information divergence and related measures of discrimination," IEEE Trans. Inf. Theory, vol.46, pp. 1602-1609, 2000.
    • (2000) IEEE Trans. Inf. Theory , vol.46 , pp. 1602-1609
    • Topsøe, F.1
  • 36
    • 0002743439 scopus 로고
    • On topological properties of divergences
    • I. Csiszár, "On topological properties of divergences," Stud. Sci. Math. Hungary, vol.2, pp. 329-339, 1967.
    • (1967) Stud. Sci. Math. Hungary , vol.2 , pp. 329-339
    • Csiszár, I.1
  • 37
    • 0000755874 scopus 로고
    • On the divergence and singularity of probability measures
    • I. Vajda, "On the divergence and singularity of probability measures," Periodica Math. Hungarica, vol.2, pp. 223-234, 1972.
    • (1972) Periodica Math. Hungarica , vol.2 , pp. 223-234
    • Vajda, I.1
  • 44
    • 85164149872 scopus 로고    scopus 로고
    • An approach to Bayesian sensitivity analysis
    • R. Weiss, "An approach to Bayesian sensitivity analysis," J. R. Statist. Soc. B, vol.58, pp. 163-177, 1996.
    • (1996) J. R. Statist. Soc. B , vol.58 , pp. 163-177
    • Weiss, R.1
  • 45
    • 0041611565 scopus 로고
    • Some conditions for consistency and uniform consistency of statistical procedures
    • C. Kraft, "Some conditions for consistency and uniform consistency of statistical procedures," Univ. California Publ. Statist., vol.1, pp. 125-142, 1955.
    • (1955) Univ. California Publ. Statist. , vol.1 , pp. 125-142
    • Kraft, C.1
  • 46
    • 18544370561 scopus 로고    scopus 로고
    • A distribution dependent refinement of Pinsker's inequality
    • E. Ordentlich and M. J. Weinberger, "A distribution dependent refinement of Pinsker's inequality," IEEE Trans. Inf. Theory, vol.51, pp. 1836-1840, 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , pp. 1836-1840
    • Ordentlich, E.1    Weinberger, M.J.2
  • 47
    • 33744461667 scopus 로고    scopus 로고
    • Some bounds for the logarithmic function
    • Article 6
    • F. Topsøe, "Some bounds for the logarithmic function," RGMIA Res. Rep. Collection, vol.7, no.2, Article 6, 2004.
    • (2004) RGMIA Res. Rep. Collection , vol.7 , Issue.2
    • Topsøe, F.1
  • 49
    • 77958612553 scopus 로고    scopus 로고
    • An improvement on Vajda's inequality
    • V. Sidoravicius and M. E. Vares, Eds. Basel: Birkhäuser
    • G. L. Gilardoni, "An improvement on Vajda's inequality," in Progr. Probabl., V. Sidoravicius and M. E. Vares, Eds. Basel: Birkhäuser, 2008, vol.60.
    • (2008) Progr. Probabl. , vol.60
    • Gilardoni, G.L.1


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