메뉴 건너뛰기




Volumn 55, Issue 12, 2009, Pages 5412-5422

Monotonic convergence in an information-theoretic law of small numbers

Author keywords

Binomial thinning; Convex order; Logarithmic Sobolev inequality; Majorization; Maximum entropy; Poisson approximation; Relative entropy; Schur concavity; Ultra log concavity

Indexed keywords

BINOMIAL THINNING; CONVEX ORDER; LOGARITHMIC SOBOLEV INEQUALITY; MAJORIZATION; MAXIMUM ENTROPY; POISSON APPROXIMATIONS; RELATIVE ENTROPY; SCHUR-CONCAVITY; ULTRA-LOG-CONCAVITY;

EID: 77951599486     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2032727     Document Type: Article
Times cited : (23)

References (42)
  • 1
    • 3042730174 scopus 로고    scopus 로고
    • On the rate of convergence in the entropic central limit theorem
    • S. Artstein, K. M. Ball, F. Barthe, and A. Naor, "On the rate of convergence in the entropic central limit theorem," Prob. Theory Rel. Fields, vol.129, no.3, pp. 381-390, 2004.
    • (2004) Prob. Theory Rel. Fields , vol.129 , Issue.3 , pp. 381-390
    • Artstein, S.1    Ball, K.M.2    Barthe, F.3    Naor, A.4
  • 2
    • 10044228109 scopus 로고    scopus 로고
    • Solution of Shannon's problem on the monotonicity of entropy
    • S. Artstein, K. M. Ball, F. Barthe, and A. Naor, "Solution of Shannon's problem on the monotonicity of entropy," J. Amer. Math. Soc., vol.17, no.4, pp. 975-982, 2004.
    • (2004) J. Amer. Math. Soc. , vol.17 , Issue.4 , pp. 975-982
    • Artstein, S.1    Ball, K.M.2    Barthe, F.3    Naor, A.4
  • 4
    • 0000061719 scopus 로고
    • Entropy and the central limit theorem
    • A. R. Barron, "Entropy and the central limit theorem," Ann. Probab., vol.14, pp. 336-342, 1986.
    • (1986) Ann. Probab. , vol.14 , pp. 336-342
    • Barron, A.R.1
  • 5
    • 84938171492 scopus 로고
    • The convolution inequality for entropy powers
    • N. M. Blachman, "The convolution inequality for entropy powers," IEEE Trans. Inf. Theory, vol.11, pp. 267-271, 1965.
    • (1965) IEEE Trans. Inf. Theory , vol.11 , pp. 267-271
    • Blachman, N.M.1
  • 6
    • 0000387123 scopus 로고    scopus 로고
    • On modified logarithmic Sobolev inequalities for Bernoulli and Poisson measures
    • S. Bobkov and M. Ledoux, "On modified logarithmic Sobolev inequalities for Bernoulli and Poisson measures," J. Funct. Anal., vol.156, no.2, pp. 347-365, 1998.
    • (1998) J. Funct. Anal. , vol.156 , Issue.2 , pp. 347-365
    • Bobkov, S.1    Ledoux, M.2
  • 7
    • 0000330875 scopus 로고
    • Unimodal, log-concave, and Pólya frequency sequences in combinatorics
    • F. Brenti, "Unimodal, log-concave, and Pólya frequency sequences in combinatorics," Mem. Amer. Math. Soc., vol.81, no.413, 1989.
    • (1989) Mem. Amer. Math. Soc. , vol.81 , Issue.413
    • Brenti, F.1
  • 8
    • 10844281118 scopus 로고    scopus 로고
    • Entropies, convexity, and functional inequalities: On φ-entropies and φ-Sobolev inequalities
    • D. Chafaï, "Entropies, convexity, and functional inequalities: On φ-entropies and φ-Sobolev inequalities," J. Math. Kyoto Univ., vol.44, no.2, pp. 325-363, 2004.
    • (2004) J. Math. Kyoto Univ. , vol.44 , Issue.2 , pp. 325-363
    • Chafaï, D.1
  • 9
    • 33846101666 scopus 로고    scopus 로고
    • Binomial-Poisson entropic inequalities and the M/M/∞ queue
    • D. Chafaï, "Binomial-Poisson entropic inequalities and the M/M/∞ queue," ESAIM Probab. Statist., vol.10, pp. 317-339, 2006.
    • (2006) ESAIM Probab. Statist. , vol.10 , pp. 317-339
    • Chafaï, D.1
  • 11
    • 34548595883 scopus 로고
    • On the product of two power series
    • H. Davenport and G. Pólya, "On the product of two power series," Canad. J. Math., vol.1, pp. 1-5, 1949.
    • (1949) Canad. J. Math. , vol.1 , pp. 1-5
    • Davenport, H.1    Pólya, G.2
  • 14
    • 0035397657 scopus 로고    scopus 로고
    • Binomial and Poisson distributions as maximum entropy distributions
    • Jul.
    • P. Harremoës, "Binomial and Poisson distributions as maximum entropy distributions," IEEE Trans. Inf. Theory, vol.47, pp. 2039-2041, Jul. 2001.
    • (2001) IEEE Trans. Inf. Theory , vol.47 , pp. 2039-2041
    • Harremoës, P.1
  • 18
    • 4544261302 scopus 로고    scopus 로고
    • Rate of convergence to Poisson law in terms of information divergence
    • P. Harremoës and P. S. Ruzankin, "Rate of convergence to Poisson law in terms of information divergence," IEEE Trans. Inf. Theory, vol.50, pp. 2145-2149, 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , pp. 2145-2149
    • Harremoës, P.1    Ruzankin, P.S.2
  • 19
    • 0001069505 scopus 로고
    • On the distribution of the number of successes in independent trials
    • W. Hoeffding, "On the distribution of the number of successes in independent trials," Ann. Math. Statist., vol.27, pp. 713-721, 1956.
    • (1956) Ann. Math. Statist. , vol.27 , pp. 713-721
    • Hoeffding, W.1
  • 20
    • 34247645455 scopus 로고    scopus 로고
    • Log-concavity and the maximum entropy property of the Poisson distribution
    • O. Johnson, "Log-concavity and the maximum entropy property of the Poisson distribution," Stoch. Processes Applicat., vol.117, no.6, pp. 791-802, 2007.
    • (2007) Stoch. Processes Applicat. , vol.117 , Issue.6 , pp. 791-802
    • Johnson, O.1
  • 21
    • 3042813990 scopus 로고    scopus 로고
    • Fisher information inequalities and the central limit theorem
    • O. Johnson and A. R. Barron, "Fisher information inequalities and the central limit theorem," Prob. Theory Rel. Fields, vol.129, no.3, pp. 391-409, 2004.
    • (2004) Prob. Theory Rel. Fields , vol.129 , Issue.3 , pp. 391-409
    • Johnson, O.1    Barron, A.R.2
  • 23
    • 0042432835 scopus 로고
    • Entropy inequalities for classes of probability distributions I. the univariate case
    • S. Karlin and Y. Rinott, "Entropy inequalities for classes of probability distributions I. The univariate case," Adv. Appl. Prob., vol.13, pp. 93-112, 1981.
    • (1981) Adv. Appl. Prob. , vol.13 , pp. 93-112
    • Karlin, S.1    Rinott, Y.2
  • 25
    • 0002303432 scopus 로고
    • Proof of an entropy conjecture of Wehrl
    • Aug.
    • E. H. Lieb, "Proof of an entropy conjecture of Wehrl," Commun. Math. Phys., vol.62, no.1, pp. 35-41, Aug. 1978.
    • (1978) Commun. Math. Phys. , vol.62 , Issue.1 , pp. 35-41
    • Lieb, E.H.1
  • 26
    • 0031206132 scopus 로고    scopus 로고
    • Ultra logconcave sequences and negative dependence
    • T. M. Liggett, "Ultra logconcave sequences and negative dependence," J. Combin. Theory Ser. A, vol.79, no.2, pp. 315-325, 1997.
    • (1997) J. Combin. Theory Ser. A , vol.79 , Issue.2 , pp. 315-325
    • Liggett, T.M.1
  • 27
    • 34447344072 scopus 로고    scopus 로고
    • Generalized entropy power inequalities and monotonicity properties of information
    • Jul.
    • M. Madiman and A. Barron, "Generalized entropy power inequalities and monotonicity properties of information," IEEE Trans. Inf. Theory, vol.53, pp. 2317-2329, Jul. 2007.
    • (2007) IEEE Trans. Inf. Theory , vol.53 , pp. 2317-2329
    • Madiman, M.1    Barron, A.2
  • 32
    • 33750630377 scopus 로고    scopus 로고
    • A free analogue of Shannon's problem on monotonicity of entropy
    • DOI 10.1016/j.aim.2006.03.014, PII S0001870806001010
    • D. Shlyakhtenko, "A free analogue of Shannon's problem on monotonicity of entropy," Adv. Math., vol.208, no.2, pp. 824-833, Jan. 2007. (Pubitemid 44688709)
    • (2007) Advances in Mathematics , vol.208 , Issue.2 , pp. 824-833
    • Shlyakhtenko, D.1
  • 34
    • 12944295719 scopus 로고
    • Some inequalities satisfied by the quantities of information of Fisher and Shannon
    • Jun.
    • A. J. Stam, "Some inequalities satisfied by the quantities of information of Fisher and Shannon," Inf. Contr., vol.2, no.2, pp. 101-112, Jun. 1959.
    • (1959) Inf. Contr. , vol.2 , Issue.2 , pp. 101-112
    • Stam, A.J.1
  • 35
    • 33748580282 scopus 로고    scopus 로고
    • Monotonic decrease of the non-Gaussianness of the sum of independent random variables: A simple proof
    • Sep.
    • A. M. Tulino and S. Verdú, "Monotonic decrease of the non-Gaussianness of the sum of independent random variables: A simple proof," IEEE Trans. Inf. Theory, vol.52, pp. 4295-4297, Sep. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , pp. 4295-4297
    • Tulino, A.M.1    Verdú, S.2
  • 36
    • 0034367243 scopus 로고    scopus 로고
    • A new modified logarithmic Sobolev inequality for Poisson point processes and several applications
    • L. Wu, "A new modified logarithmic Sobolev inequality for Poisson point processes and several applications," Probab. Theory Rel. Fields, vol.118, no.3, pp. 427-438, 2000.
    • (2000) Probab. Theory Rel. Fields , vol.118 , Issue.3 , pp. 427-438
    • Wu, L.1
  • 37
    • 46749147708 scopus 로고    scopus 로고
    • On the maximum entropy properties of the binomial distribution
    • Jul.
    • Y. Yu, "On the maximum entropy properties of the binomial distribution," IEEE Trans. Inf. Theory, vol.54, pp. 3351-3353, Jul. 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , pp. 3351-3353
    • Yu, Y.1
  • 38
    • 59549087228 scopus 로고    scopus 로고
    • On an inequality of Karlin and Rinott concerning weighted sums of i.i.d. random variables
    • Y. Yu, "On an inequality of Karlin and Rinott concerning weighted sums of i.i.d. random variables," Adv. Appl. Prob., vol.40, no.4, pp. 1223-1226, 2008.
    • (2008) Adv. Appl. Prob. , vol.40 , Issue.4 , pp. 1223-1226
    • Yu, Y.1
  • 39
    • 68249133772 scopus 로고    scopus 로고
    • On the entropy of compound distributions on nonnegative integers
    • Aug.
    • Y. Yu, "On the entropy of compound distributions on nonnegative integers," IEEE Trans. Inf. Theory, vol.55, pp. 3645-3650, Aug. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , pp. 3645-3650
    • Yu, Y.1
  • 40
    • 57149144664 scopus 로고    scopus 로고
    • Complete monotonicity of the entropy in the central limit theorem for gamma and inverse Gaussian distributions
    • Y. Yu, "Complete monotonicity of the entropy in the central limit theorem for gamma and inverse Gaussian distributions," Stat. Prob. Lett., vol.79, pp. 270-274, 2009.
    • (2009) Stat. Prob. Lett. , vol.79 , pp. 270-274
    • Yu, Y.1
  • 41
    • 77957570446 scopus 로고    scopus 로고
    • Relative log-concavity and a pair of triangle inequalities
    • to be published
    • Y. Yu, "Relative log-concavity and a pair of triangle inequalities," Bernoulli J., to be published.
    • Bernoulli J.
    • Yu, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.